The growth index $γ_L$ was proposed to investigate the possible deviation from the standard $Λ$CDM model and Einstein's gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space distortion, one can understand the evolution of density contrast through $fσ_8(z)$, where $f(z)=d\ln δ/d \ln a$ is the growth rate of matter and $σ_8(z)$ is the rms amplitude of the density contrast $δ$ at the comoving $8h^{-1}$ Mpc scale. In this paper, we use the redshift space distortion data points to study the growth index on the bases of Einstein's gravity theory and a modified gravity theory under the assumption of $f=Ω_m(a)^{γ_L}$. The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3, cosmic microwave background radiation data from {\it Planck} and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we found the $γ_L$ values for Einstein's gravity with a cosmological constant, $w=constant$ dark energy and a modified gravity theory in the $1,2,3σ$ regions respectively: $0.675_{-0.0662-0.120-0.155}^{+0.0611+0.129+0.178}$, $0.745_{-0.0819-0.146-0.190}^{+0.0755+0.157+0.205}$ and $0.555_{-0.0167-0.0373-0.0516}^{+0.0193+0.0335+0.0436}$. In the Einstein's gravity theory, the values of growth index $γ_L$ show almost $2σ$ deviation from the theoretical prediction 6/11 for the $Λ$CDM model. However in the modified gravity framework, a deviation from the Einstein's relativity is not detected in $1σ$ region. That implies that the currently available cosmic observations don't expect an alternative modified gravity theory beyond the $Λ$CDM model under Einstein's gravity, but that the simple assumption of $f=Ω_m^{γ_L}$ should be improved.
We perform a meta-study of recently published Redshift Space Distortion (RSD) measurements of the cosmological growth rate, f(z) σ_8(z). We analyse the latest results from the 6dFGS, BOSS, LRG, WiggleZ and VIPERS galaxy redshift surveys, and compare the measurements to expectations from Planck. In this Letter we point out that the RSD measurements are consistently lower than the values expected from Planck, and the relative scatter between the RSD measurements is lower than expected. A full resolution of this issue may require a more robust treatment of non-linear effects in RSD models, althou…
In this paper, a unified dark fluid with constant adiabatic sound speed is decomposed into cold dark matter interacting with vacuum energy. Based on Markov chain Monte Carlo method, we constrain this model by jointing the geometry and dynamical measurement. The geometry test includes cosmic microwave background radiation from \textit{Planck}, baryon acoustic oscillation, and type Ia supernovae; the dynamic measurement is $fσ_8(z)$ data points which is obtained from the growth rate via redshift-space distortion, and $σ_8(z)$ is the root-mean-square amplitude of the density contrast $δ$ at the c…
Planck favours a negative running of the spectral index, with the likelihood being dominated by low multipoles $l \lesssim 50$ and no preference for running at higher $l$. A negative spectral index is also necessary for the 2-$σ$ Planck upper bound on the tensor-to-scalar ratio $r$ to be consistent with values significantly larger than 0.1. Planck has also observed a hemispherical asymmetry of the CMB power spectrum, again mostly at low multipoles. Here we consider whether the physics responsible for the hemispherical asymmetry could also account for the negative running of the spectral index …
In this paper, we compare brane inflation models with the Planck data and the pre-Planck data (which combines WMAP, ACT, SPT, BAO and H0 data). The Planck data prefer a spectral index less than unity at more than 5σconfidence level, and a running of the spectral index at around 2σconfidence level. We find that the KKLMMT model can survive at the level of 2σonly if the parameter $β$ (the conformal coupling between the Hubble parameter and the inflaton) is less than $\mathcal{O}(10^{-3})$, which indicates a certain level of fine-tuning. The IR DBI model can provide a slightly larger negative run…
We revisit spectator field models including curvaton and modulated reheating scenarios, specifically focusing on their viability in the new Planck era, based on the derived expression for the spectral index in general spectator field models. Importantly, the recent Planck observations give strong preference to a red-tilted power spectrum, while the spectator field models tend to predict a scale-invariant one. This implies that, during inflation, either (i) the Hubble parameter varies significantly as in chaotic inflation, or (ii) a scalar potential for the spectator field has a relatively larg…
We present a new measurement of structure growth at $z \simeq 0.08$ obtained by correlating the cosmic microwave background (CMB) lensing potential map from the \textit{Planck} satellite with the angular distribution of the 2MASS Photometric Redshift galaxies. After testing for, and finding no evidence for systematic effects, we calculate the angular auto- and cross-power spectra. We combine these spectra to estimate the amplitude of structure growth using the bias-independent $D_G$ estimator introduced by Giannantonio et al. 2016. We find that the relative amplitude of $D_G$ with respect to t…
We study is some detail the Cosmology of Oscillating Dark Energy described by concrete equations-of-state investigated recently in the literature. In particular, at the background level we compute the statefinder parameters, while at the level of linear cosmological perturbations we compute the growth index $γ$ as well as the combination parameter $A=f σ_8$. The comparison with $Λ$CDM is made as well.
Understanding the properties of dust emission in the microwave domain is an important premise for the next generation of cosmic microwave background (CMB) experiments, devoted to the measurement of the primordial $B$-modes of polarization. In this paper, we compare three solutions to thermal dust emission by the Planck Collaboration \cite{PlanckDust03,planck_16,planck_com} to point out significant differences between their respective parameters (the spectral index $β$, the optical depth $τ$ and the dust temperature $T_d$). These differences originate from e.g. the priors on the parameters or t…
We present numerical calculation of the evolution of a background space-time metric and sub-horizon matter density perturbations in viable $f(R)$ gravity models of present dark energy and cosmic acceleration. We found that viable models generically exhibit recent crossing of the phantom boundary $w_{DE}=-1$. Moreover, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves non-monotonically with time and may even become negative.
The Atacama Cosmology Telescope: High-redshift measurement of structure growth from the cross-correlation of Quaia quasars and CMB lensing from ACT DR6 and $\textit{Planck}$ PR4
We present the analytical solutions for the evolution of matter density perturbations, for a model with a constant dark energy equation of state $w$ but when the effects of the dark energy perturbations are properly taken into account. We consider two cases, the first when the sound speed of the perturbations is zero $c_s^2=0$ and the general case $0<c_s^2 \leq 1$. In the first case our solution is exact, while in the second case we found an approximate solution which works to better than $0.3\%$ accuracy for $k>10 H_0$ or equivalently $k/h>0.0033 \textrm{Mpc}^{-1}$. We also estimate the corre…
We show that in clustering dark energy models the growth index of linear matter perturbations, $γ$, can be much lower than in $Λ$CDM or smooth quintessence models and present a strong variation with redshift. We find that the impact of dark energy perturbations on $γ$ is enhanced if the dark energy equation of state has a large and rapid decay at low redshift. We study four different models with these features and show that we may have $0.33<γ\left(z\right)<0.48$ at $0<z<3$. We also show that the constant $γ$ parametrization for the growth rate, $f=d\lnδ_{m}/d\ln a=Ω_{m}^γ$, is a few percent i…
Using Planck polarization data, we search for and constrain spatial variations of the polarized dust foreground for cosmic microwave background (CMB) observations, specifically in its spectral index, $β_d$. Failure to account for such variations will cause errors in the foreground cleaning that propagate into errors on cosmological parameter recovery from the cleaned CMB map. It is unclear how robust prior studies of the Planck data which constrained $β_d$ variations are due to challenges with noise modeling, residual systematics, and priors. To clarify constraints on $β_d$ and its variation, …
In this Letter we point out that redshift surveys can break the degeneracy between the galaxy bias, the power spectrum normalization, σ_{8,0} and the growth factor, without the need for external information by using a simple and rather general parametrization for the growth rate, the well known γ-parametrization and measuring the power spectrum at least at two different redshifts. We find that in next-generation surveys like Euclid, σ_{8,0} and γcan be measured to within 1% and 5%, respectively, while the bias b(z) can be measured to within 1-2% in each of 14 equal-width redshift bins spanning…
We study a dark energy model with non-zero anisotropic stress, either linked to the dark energy density or to the dark matter density. We compute approximate solutions that allow to characterise the behaviour of the dark energy model and to assess the stability of the perturbations. We also determine the current limits on such an anisotropic stress from the cosmic microwave background data by the Planck satellite, and derive the corresponding constraints on the modified growth parameters like the growth index, the effective Newton's constant and the gravitational slip.
The Atacama Cosmology Telescope DR6 and DESI: Structure growth measurements from the cross-correlation of DESI Legacy Imaging galaxies and CMB lensing from ACT DR6 and Planck PR4
We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data.…
Measurements of the growth index $γ(z)$ provide a clue as to whether Einstein's field equations encompass gravity also on large cosmic scales, those where the expansion of the universe accelerates. We show that the information encoded in this function can be satisfactorily parameterized using a small set of coefficients $γ_i$ in such a way that the true scaling of the growth index is recovered to better than $1\%$ in most dark energy and dark gravity models. We find that the likelihood of current data is maximal for $γ_0=0.74\pm 0.44$ and $γ_1=0.01\pm0.46$, a measurement compatible with the $Λ…
Thomson optical depth tau measurements from Planck provide new insights into the reionization of the universe. In pursuit of model-independent constraints on the properties of the ionising sources, we determine the empirical evolution of the cosmic ionizing emissivity. We use a simple two-parameter model to map out the evolution in the emissivity at z>~6 from the new Planck optical depth tau measurements, from the constraints provided by quasar absorption spectra and from the prevalence of Ly-alpha emission in z~7-8 galaxies. We find the redshift evolution in the emissivity dot{N}_{ion}(z) req…
In order to investigate the origin of the ongoing tension between the amplitude of matter fluctuations measured by weak lensing experiments at low redshifts and the value inferred from the cosmic microwave background anisotropies, we reconstruct the evolution of this amplitude from $z\sim2$ using existing large-scale structure data. To do so, we decouple the linear growth of density inhomogeneities from the background expansion, and constrain its redshift dependence making use of a combination of 6 different data sets, including cosmic shear, galaxy clustering and CMB lensing. We analyze these…
We consider the behavior of spherically symmetric Einasto halos composed of gravitating particles in the Fokker-Planck approximation. This approach allows us to consider the undesirable influence of close encounters in the N-body simulations more adequately than the generally accepted criteria. The Einasto profile with index $n \approx 6$ is a stationary solution of the Fokker-Planck equation in the halo center. There are some reasons to believe that the solution is an attractor. Then the Fokker-Planck diffusion tends to transform a density profile to the equilibrium one with the Einasto index…
I present a large set of high resolution simulations, called CosmicGrowth Simulations, which were generated with either 8.6 billion or 29 billion particles. As the nominal cosmological model that can match nearly all observations on cosmological scales, I have adopted a flat Cold Dark Matter (CDM) model with a cosmological constant $Λ$ ($Λ$CDM). The model parameters have been taken either from the latest result of the WMAP satellite (WMAP $Λ$CDM) or from the first year's result of the Planck satellite (Planck $Λ$CDM). Six simulations are produced in the $Λ$CDM models with two in the Planck mod…
An inflationary model in the framework of noncommutative space-time may generate a nontrivial running of the scalar spectral index, but usually induces a large tensor-to-scalar ratio simultaneously. With the latest observational data from the Planck mission, we reexamine the inflationary scenarios in a noncommutative space-time. We find that either the running of the spectral index is tiny compared with the recent observational result, or the tensor-to-scalar ratio is too large to allow a sufficient number of $e$-folds. As examples, we show that the chaotic and power-law inflation models with …
We analyze the claimed tension between redshift space distorsions measurements of $f(z)σ_8(z)$ and the predictions of standard $Λ$CDM (Planck 2015 and 2018) cosmology. We consider a dataset consisting of 17 data points extending up to redshift $z=1.52$ and corrected for the Alcock-Paczynski effect. Thus, calculating the evolution of the growth factor in a $w$CDM cosmology, we find that the tension for the best fit parameters $w$, $Ω_m$ and $σ_8$ with respect to the Planck 2018 $Λ$CDM parameters is below $2σ$ in all the marginalized confidence regions.
Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from {\it Planck}. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models also can amplify isocurvature perturbations, which could account for the low power recently observed in the CMB power spectrum at low multipoles. Future measur…
Variance of dust temperature and spectral index in Planck polarization data using spin-moment expansion
Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay（空间天体物理研究所，法国国家科学研究中心，巴黎南大学，巴黎萨克雷大学）；Laboratoire Univers et Particules de Montpellier, Université de Montpellier, CNRS/IN2P2（蒙彼利埃宇宙与粒子实验室，蒙彼利埃大学，法国国家科学研究中心/法国国家核子和粒子物理研究所）；International School for Advanced Studies (SISSA)（高级国际研究学院）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste（意大利国家核物理研究所，的里雅斯特分部）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）；IRAP, Université de Toulouse, CNRS, CNES, UPS（天体物理学研究所，图卢兹大学，法国国家科学研究中心，法国国家空间研究中心）；Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，巴黎高等师范学院，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎大学）；Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院）；INAF - Osservatorio Astronomico di Cagliari（意大利国家天体物理研究所，卡利亚里天文台）；Laboratoire d’Océanographie Physique et Spatiale (LOPS), Univ. Brest, CNRS, Ifremer, IRD（物理与空间海洋学实验室，布雷斯特大学，法国国家科学研究中心，法国海洋开发研究院，法国农业食品与林业研究发展中心）
We place tight constraints on the growth index $γ$ by using the recent growth history results of 2dFGRS, SDSS-LRG, VIMOS-VLT deep Survey (VVDS) and {\em WiggleZ} datasets. In particular, we investigate several parametrizations of the growth index $γ(z)$, by comparing their cosmological evolution using observational growth rate data at different redshifts. Utilizing a standard likelihood analysis we find that the use of the combined growth data provided by the 2dFGRS, SDSS-LRG, VVDS and {\em WiggleZ} galaxy surveys, puts the most stringent constraints on the value of the growth index. As an exa…
We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence. In order to maximize the independence of the datapoints we also construct a subsample of this compilation (`Gold' growth dataset) which consists of 18 datapoints. We test the consistency of this dataset with the best fit Planck15/$Λ$CDM parameters in the context of General Relativity (GR) using the evolution equation for the growth factor $δ(a)$ with a $w$CDM background. We find tension at the $\sim 3 σ$ level between the best fit parameters $w$ (the dark…
We use Gaussian Processes to map the expansion history of the universe in a model independent manner from the Union2.1 supernovae data and then apply these reconstructed results to solve for the growth history. By comparing this to BOSS and WiggleZ large scale structure data we examine whether growth is determined wholly by expansion, with the measured gravitational growth index testing gravity without assuming a model for dark energy. A further model independent analysis looks for redshift dependent deviations of growth from the general relativity solution without assuming the growth index fo…
We perform the first fit to the anisotropic clustering of SDSS-III CMASS DR10 galaxies on scales of ~ 0.8 - 32 Mpc/h. A standard halo occupation distribution model evaluated near the best fit Planck LCDM cosmology provides a good fit to the observed anisotropic clustering, and implies a normalization for the peculiar velocity field of M ~ 2 x 10^13 Msun/h halos of f*sigma8(z=0.57) = 0.450 +/- 0.011. Since this constraint includes both quasi-linear and non-linear scales, it should severely constrain modified gravity models that enhance pairwise infall velocities on these scales. Though model de…
We investigate the growth of matter fluctuations in holographic dark energy cosmologies. First we use an overall statistical analysis involving the latest observational data in order to place constraints on the cosmological parameters. Then we test the range of validity of the holographic dark energy models at the perturbation level and its variants from the concordance $Λ$ cosmology. Specifically, we provide a new analytical approach in order to derive, for the first time, the growth index of matter perturbations. Considering a homogeneous holographic dark energy we find that the growth index…
We have put forward a new unified framework which provides a consistent and rather complete account of the growth index of matter perturbations in the regime where the dark energy is allowed to have clustering. In particular, we find that the growth index is not only affected by the cosmological parameters but rather it depends on the choice of the considered dark energy (homogeneous or clustered). Using the {\em Planck} priors and performing a standard $χ^2$-minimization between theoretical expectations and growth data, we statistically quantify the ability of the growth index to represent th…
We obtain the exact analytic form of the growth index at present epoch ($a=1$) in a flat universe with the cosmological constant ({\it i.e.} the dark energy with its equation of state $ω_{de} = -1$). For the cosmological constant, we obtain the exact value of the current growth index parameter $γ= 0.5547$, which is very close to the well known value 6/11. We also obtain the exact analytic solution of the growth factor for $ω_{de}$ = -1/3 or -1. We investigate the growth index and its parameter at any epoch with this exact solution. In addition to this, we are able to find the exact $Ω_{m}^{0}$…
We use current and future simulated data of the growth rate of large scale structure in combination with data from supernova, BAO, and CMB surface measurements, in order to put constraints on the growth index parameters. We use a recently proposed parameterization of the growth index that interpolates between a constant value at high redshifts and a form that accounts for redshift dependencies at small redshifts. We also suggest here another exponential parameterization with a similar behaviour. The redshift dependent parametrizations provide a sub-percent precision level to the numerical grow…
We derive the analytic formula of the growth index for $f(R)$ dark energy model where the effect on the growth of matter density perturbation $δ_m$ from modified gravity (MG) is encoded in the effective Newton coupling constant $G_{\rm eff}$ in MG (or equivalently $g\equiv {G_{\rm eff}/ G}$). Based on the analytic formula, we propose that the parameter $g$ can be directly figured out by comparing the observed growth rate $f_g\equiv d\lnδ_m/d\ln a$ to the prediction of $f_g$ in general relativity.
Rubano and Barrow have discussed the emergence of a dark energy, with late-time cosmic acceleration arising from a self-interacting homogeneous scalar field with a potential of hyperbolic power type. Here, we study the evolution of this scalar field potential back in the inflationary era. Using the hyperbolic power potential in the framework of inflation, we find that the main slow-roll parameters, like the scalar spectral index, the running of the spectral index and the tensor-to-scalar fluctuation ratio can be computed analytically. Finally, in order to test the viability of this hyperbolic …
The gravitational growth index formalism provides a model independent way to look for deviations from general relativity by testing dark energy physics distinct from its effects on the cosmic expansion history. Here we extend the approach to incorporate an early time parameter g_star in addition to the growth index in describing the growth of large scale structure. We illustrate its utility for models with modified gravity at high redshift, early acceleration, or early dark energy. Future data will have the capability to constrain the dark energy equation of state, the growth index gamma, and …
We study the main cosmological properties of the agegraphic dark energy model at the expansion and perturbation levels. Initially, using the latest cosmological data we implement a joint likelihood analysis in order to constrain the cosmological parameters. Then we test the performance of the agegraphic dark energy model at the perturbation level and we define its difference from the usual $Λ$CDM model. Within this context, we verify that the growth index of matter fluctuations depends on the choice of the considered agegraphic dark energy (homogeneous or clustered). In particular, assuming a …
We explore a fluid description of the inflationary universe. In particular, we investigate a fluid model in which the equation of state (EoS) for a fluid includes bulk viscosity. We find that the three observables of inflationary cosmology: the spectral index of the curvature perturbations, the tensor-to-scalar ratio of the density perturbations, and the running of the spectral index, can be consistent with the recent Planck results. We also reconstruct the explicit EoS for a fluid from the spectral index of the curvature perturbations compatible with the Planck analysis. In the reconstructed …
We revisit a single-field new inflation model based on a discrete R symmetry. Interestingly, the inflaton dynamics naturally leads to a heavy gravitino of mass m_3/2 = O(1-100) TeV, which is consistent with the standard-model like Higgs boson of mass mh = 126 GeV. However, the predicted spectral index n_s = 0.94 is in tension with the Planck result, n_s = 0.9603+-0.073. We show that the spectral index can be increased by allowing a small constant term in the superpotential during inflation. The required size of the constant is close to the largest allowed value for successful inflation, and it…
The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio $r=0$ ruled out at $7σ$ level. The consistency of this large value of $r$ with the {\em Planck} data requires a large negative running $n'_s$ of the scalar spectral index. Herein we propose two types of the single field inflation models with simple potentials to study the possibility of the consistency of the models with the BICEP2 and {\em Planck} observations. One type of model suggested herein is realized in the supergravity model building. These models fail to provide the needed $n…
Evolution of a background space-time metric and sub-horizon matter density perturbations in the Universe is numerically analyzed in viable $f(R)$ models of present dark energy and cosmic acceleration. It is found that viable models generically exhibit recent crossing of the phantom boundary $w_{\rm DE}=-1$. Furthermore, it is shown that, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves non-monotonically with time and may even become negative temporarily.
Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0σ$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $Λ$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a po…
We use the clustering properties of Luminous Red Galaxies (LRGs) and the growth rate data provided by the various galaxy surveys in order to constrain the growth index ($γ$) of the linear matter fluctuations. We perform a standard $χ^2$-minimization procedure between theoretical expectations and data, followed by a joint likelihood analysis and we find a value of $γ=0.56\pm 0.05$, perfectly consistent with the expectations of the $Λ$CDM model, and $Ω_{m0} =0.29\pm 0.01$, in very good agreement with the latest Planck results. Our analysis provides significantly more stringent growth index const…
Three decades ago Heath found the integral form of the exact analytic growing mode solution of the linear density perturbation $δ$ on sub-horizon scales including the cosmological constant or the curvature term. Recently, we obtained the exact analytic form of this solution in our previous work \cite{SK}. Interestingly, we are able to extend this solution for general dark energy models with the constant equation of state $ω_{de}$ in a flat universe. This analytic solution provides the accurate and efficient tools for probing the properties of dark energy models such as the behavior of the grow…
We investigate the axion dark matter scenario (ADM), in which axions account for all of the dark matter in the Universe, in light of the most recent cosmological data. In particular, we use the Planck temperature data, complemented by WMAP E-polarization measurements, as well as the recent BICEP2 observations of B-modes. Baryon Acoustic Oscillation data, including those from the Baryon Oscillation Spectroscopic Survey, are also considered in the numerical analyses. We find that, in the minimal ADM scenario, the full dataset implies that the axion mass m_a = 82.2 pm 1.1 μeV (corresponding to th…
We analyze the global behaviour of the growth index of cosmic inhomogeneities in an isotropic homogeneous universe filled by cold non-relativistic matter and dark energy (DE) with an arbitrary equation of state. Using a dynamical system approach, we find the critical points of the system. That unique trajectory for which the growth index $γ$ is finite from the asymptotic past to the asymptotic future is identified as the so-called heteroclinic orbit connecting the critical points $(Ω_m=0,~γ_{\infty})$ in the future and $(Ω_m=1,~γ_{-\infty})$ in the past. The first is an attractor while the sec…
The accelerated cosmic expansion could be due to dark energy within general relativity (GR), or modified gravity. It is of interest to differentiate between them, by using both the expansion history and the growth history. In the literature, it was proposed that the growth index $γ$ is useful to distinguish these two scenarios. In this work, we consider the non-parametric reconstruction of the growth index $γ$ as a function of redshift $z$ from the latest observational data as of July 2018 via Gaussian Processes. We find that $f(R)$ theories and dark energy models within GR (especially $Λ$CDM)…
The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration. We suggest here parameterizations of the growth index as functions of the redshift. The first one is given by $γ(a)=\tildeγ(a) \frac{1}{1+(a_{_{ttc}}/a)}+γ_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tildeγ(a)=γ_{_{late}}(a)= γ_0 + (1-a) γ_a$ and a high redshift $γ_{_{early}}$ constant value…
We revisit cosmic microwave background (CMB) constraints on the abundance of millicharged particles based on the Planck data. The stringent limit Omega_{mcp}h^2 < 0.001 (95% CL) may be set using the CMB data alone if millicharged particles participate in the acoustic oscillations of baryon-photon plasma at the recombination epoch. The latter condition is valid for a wide region of charges and masses of the particles. Adding the millicharged component to LCDM shifts prefered scalar spectral index of primordial perturbations to somewhat larger values as compared to minimal model, even approachin…
We study how the cosmological constraints from growth data are improved by including the measurements of bias from Dark Energy Survey (DES). In particular, we utilize the biasing properties of the DES Luminous Red Galaxies (LRGs) and the growth data provided by the various galaxy surveys in order to constrain the growth index ($γ$) of the linear matter perturbations. Considering a constant growth index we can put tight constraints, up to $\sim 10\%$ accuracy, on $γ$. Specifically, using the priors of the Dark Energy Survey and implementing a joint likelihood procedure between theoretical expec…
We derive for the first time the growth index of matter perturbations of the FLRW flat cosmological models in which the vacuum energy depends on redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which apart from a leading constant term $Λ_0$ there is also a $H^{2}$-dependence in the functional form of vacuum, namely $Λ(H)=Λ_{0}+3ν(H^{2}-H^{2}_{0})$. Since $|ν|\ll1$ this form endows the vacuum energy of a mild dynamics which affects the evolution of the main cosmological observables at the background and perturbation levels. Specifically, at th…
Under the commonly used assumption that clumped objects can be well described by a spherical top-hat matter density profile, we investigate the evolution of the cosmic growth index in clustering dark energy (CDE) scenarios on sub-horizon scales. We show that the evolution of the growth index $γ(z)$ strongly depends on the equation-of-state (EoS) parameter and on the clustering properties of the dark energy (DE) component. Performing a $χ^2$ analysis, we show that CDE models have a better fit to observational growth rate data points with respect to the concordance $Λ$CDM model. We finally deter…
In the lights of current BICEP2 observations accompanied with the PLANCK satellite results, it has been observed that the simple single field chaotic inflationary models provide a good agreement with their spectral index n_s and large tensor-to-scalar ratio r (0.15 <r <0.26). To explore the other simple models, we consider the fractional-chaotic inflationary potentials of the form V_0 phi^(a/b) where a and b are relatively prime. We show that such kind of inflaton potentials can be realized elegantly in the supergravity framework with generalized shift symmetry and a nature bound a/b < 4 for c…
