Recently released Planck data implies a smaller Hubble constant $H_0$ than that from Hubble Space Telescope project (HST) and a larger percentage of the matter components $Ω_m$ compared to Supernova Legacy Survey (SNLS) in $Λ$CDM model. In this paper we found that even though the tension on $H_0$ between Planck and HST can be relaxed if the dark radiation is introduced ($ΔN_{\rm eff}=0.536_{-0.224}^{+0.229}$ at $68\%$ CL from the datasets of Planck+WMAP Polarization (WP)+baryon acoustic oscillation (BAO)+the combination of supernova Union2.1 compilation of 580 SNe (Union2.1)+HST), $Ω_m$ from Planck is still not nicely compatible with that from SNLS. The tensions between Planck and other astrophysical datasets can be significantly relaxed in $w$CDM model, and the combination of these datasets prefers a phantom-like dark energy at more than $95\%$ CL: $w=-1.15\pm 0.07$ and $w=-1.16\pm 0.06$ at $68\%$ CL from Planck+WP+BAO+Union2.1+HST and Planck+WP+BAO+SNLS+HST respectively. From the statistical point of view, there is no evidence for a time-evolving equation of state ($Δχ^2=-0.3$ compared to a constant equation of state for the combination of Planck+WP+BAO+SNLS+HST).
The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in CMB power spectra compared to that predicted in the standard $Λ$CDM model. A closed universe can provide a physical explanation for this effect, with the Planck CMB spectra now preferring a positive curvature at more than $99 \%$ C.L. Here we further investigate the evidence for a closed universe from Planck, showing that positive curvature naturally explains the anomalous lensing amplitude and demonstrating that it also removes a well-known tension within the Planck data set concerning the val…
The physical history of the Universe is completed by including the quantum planckian and trans-planckian phase before Inflation in the Standard Model of the Universe in agreement with observations. A new quantum precursor phase appears beyond the Planck scale. We extend de Sitter universe to the quantum domain: classical-quantum de Sitter duality. As a result: The classical and quantum dual de Sitter Temperatures and Entropies are naturally included, and the different (classical, semiclassical, quantum planckian and super-planckian) de Sitter regimes characterized in a precise and unifying way…
The classical Friedmann-Lemaître equations are solved using a corrected version of Planck's radiation law. The function curves of the scale parameter a(t) and the variations with temperature a(T) and t(T) are given. It is shown that a reasonable cosmological evolution is only possible in case of flat spatial slices (k=0). The initial singularity is avoided. Horizon and flatness problems do not exist. For low temperatures compared with the Planck Temperatur, the equations yield the usual course of expansion of the standard FLRW model for a radiation universe with k=0 and p=u(T)/3.
We compared the Planck 2018 data on the large-scale anisotropies in the cosmic microwave background to the results obtained in the slightly anisotropic ellipsoidal universe. We focused on the quadrupole temperature correlations to better constrain the eccentricity at decoupling and the direction of the symmetry axis. We found that the quadrupole TE and EE temperature correlations in the ellipsoidal universe are still in reasonable agreement with the Planck 2018 data. We suggested that an experimental estimate of the average large-scale polarisation by the Planck Collaboration could confirm or …
We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10-10^{4} compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should antici…
We show that results from the Planck satellite reported in 2013 are consistent with the simplest cyclic models for natural parameter ranges i.e., order unity dimensionless coefficients, assuming the standard entropic mechanism for generating curvature perturbations. With improved precision, forthcoming results from Planck and other experiments should be able to test the parameter ranges by confirming or refuting the core predictions - i.e., no observable primordial B-mode polarization and detectable local non-gaussianity. A new prediction, given the Planck 2013 constraints on the bispectrum, i…
Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, ϕ)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $ϕ$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop q…
The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures continue to be challenged. But new developments in the analysis of the most recent Planck data suggest that the primordial power spectrum has a cutoff associated with the very first quantum fluctuation to have emerged into the semi-classical universe from the Planck domain at about the Planck time. In this paper, we examine the implications of this result o…
Data from the Planck satellite imply new dates for the major eras of the universe. The era of radiation ended 50,150 years after inflation and the era of matter 10.31 billion years after inflation or 3.51 billion years ago.
We revisit constraints on the (pseudo)conformal Universe from the non-observation of statistical anisotropy in the Planck data. The quadratic maximal likelihood estimator is applied to the Planck temperature maps at frequencies 143 GHz and 217 GHz as well as their cross-correlation. The strongest constraint is obtained in the scenario of the (pseudo)conformal Universe with a long intermediate evolution after conformal symmetry breaking. In terms of the relevant parameter (coupling constant), the limit is h^2 <0.0013 at 95% C.L. (using the cross-estimator). The analogous limit is much weaker in…
We investigate the descriptions for the observables of inflationary models, in particular, the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and $F(R)$ gravity theories through the reconstruction methods. Furthermore, the perfect fluid and $F(R)$ gravity descriptions of inflation are compared with the recent cosmological observations such as the Planck satellite and BICEP2 experiment. It is demonstrated with explicit examples that perfect fluid may lead to the inflationary universe consiste…
We investigate a fluid description of inflationary cosmology. It is shown that the three observables of the inflationary universe: 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 compatible with the Planck analysis. In addition, we reconstruct the equation of state (EoS) for a fluid from the spectral index of the curvature perturbations consistent with the Planck results. We explicitly demonstrate that the universe can gracefully exit from inflation in the reconstructed fluid models. Furth…
We revisit the observational constraints on spatial curvature following recent claims that the Planck data favour a closed Universe. We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, though because of a geometrical degeneracy cosmic microwave background spectra on their own do not lead to tight constraints on the curvature density parameter Omega_K. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, the Universe is …
Inflationary theory predicts that the observable Universe should be very close to flat, with a spatial-curvature parameter |Omega_K| < 10^-4. The WMAP satellite currently constrains |Omega_K| < 0.01, and the Planck satellite will be sensitive to values near 10^-3. Suppose that Planck were to find Omega_K to be non-zero at this level. Would this necessarily be a serious problem for inflation? We argue that an apparent departure from flatness could be due either to a local (wavelength comparable to the observable horizon) inhomogeneity, or a truly superhorizon departure from flatness. If there i…
Recent measurements of the Cosmic Microwave Anisotropies power spectra measured by the Planck satellite show a preference for a closed universe at more than $99 \%$ Confidence Level. Such a scenario is however in disagreement with several low redshift observables, including luminosity distances of Type Ia Supernovae. Here we show that Interacting Dark Energy (IDE) models can ease the discrepancies between Planck and Supernovae Ia data in a closed Universe. Therefore IDE cosmologies remain as very appealing scenarios, as they can provide the solution to a number of observational tensions in dif…
Inflation is considered as the best theory of the early universe by a very large fraction of cosmologists. However, the validity of a scientific model is not decided by counting the number of its supporters and, therefore, this dominance cannot be taken as a proof of its correctness. Throughout its history, many criticisms have been put forward against inflation. The final publication of the Planck Cosmic Microwave Background data represents a benchmark time to study their relevance and to decide whether inflation really deserves its supremacy. In this paper, we categorize the criticisms again…
In this paper it is suggested that inclusion of mutual gravitational interactions among the particles in the early dense universe can lead to a 'pre-big bang' scenario, with particle masses greater than the Planck mass implying an accelerating phase of the universe, which then goes into the radiation phase when the masses fall below the Planck mass. The existence of towers of states of such massive particles (i.e. multiples of Planck mass) as implied in various unified theories, provides rapid acceleration in the early universe, similar to the usual inflation scenario, but here the expansion r…
A non-minimally coupled scalar field can have, in principle, a negative effective Planck mass squared which depends on the scalar field. Surprisingly, an isotropic and homogeneous cosmological universe with a non-minimally coupled scalar field is perfectly smooth as the rolling scalar field causes the effective Planck mass to change sign and pass through zero. However, we show that any small deviations from homogeneity diverge as the effective Planck mass vanishes, with catastrophic consequences for the cosmology. The physical origin of the divergence is due to the presence of non-zero scalar …
We use the latest Planck constraints, and in particular constraints on the derived parameters (Hubble constant and age of the Universe) for the local universe and compare them with local measurements of the same quantities. We propose a way to quantify whether cosmological parameters constraints from two different experiments are in tension or not. Our statistic, T, is an evidence ratio and therefore can be interpreted with the widely used Jeffrey's scale. We find that in the framework of the LCDM model, the Planck inferred two dimensional, joint, posterior distribution for the Hubble constant…
Recent Planck data confirm that the cosmic microwave background displays the quadru-pole power suppression together with large scale anomalies. Progressing from previous results, that focused on the quadrupole anomaly, we strengthen the proposal that the slightly anisotropic ellipsoidal universe may account for these anomalies. We solved at large scales the Boltzmann equation for the photon distribution functions by taking into account both the effects of the inflation produced primordial scalar perturbations and the anisotropy of the geometry in the ellipsoidal universe. We showed that the lo…
The curvature parameter tension between Planck 2018, cosmic microwave background lensing, and baryon acoustic oscillation data is measured using the suspiciousness statistic to be 2.5 to 3$σ$. Conclusions regarding the spatial curvature of the universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50:1 against a flat universe, and over 2000:1 against an open universe.
We present proof of principle for a two way interplay between physics at very early Universe and late time observations. We find a relation between primordial mechanisms responsible for large scale power suppression in the primordial power spectrum and the value of reionization optical depth $τ$. Such mechanisms can affect the estimation of $τ$. We show that using future measurements of $τ$, one can obtain constraints on the pre-inflationary dynamics, providing a new window on the physics of the very early Universe. Furthermore, the new, re-estimated $τ$ can potentially resolve moderate discre…
In this work, we constrain the spectral index $n_t$ of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, and the BICEP2 data. We call this model the $Λ$CDM+$r$+$ν_s$+$n_t$ model. The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data, and thus can reduce the possible effects of this tension on the fit results of $n_t$. To constrain the parameters of sterile neutrino, we also utilize t…
We consider an ultra-light scalar field with a mass comparable to (or lighter than) the Hubble parameter of the present universe, and calculate the time evolution of the energy-momentum tensor of the vacuum fluctuations generated during and before inflation until the late-time radiation-dominated and matter-dominated universe. The equation of state changes from $w=1/3$ in the early universe to $w=-1$ at present, and it can give a candidate for the dark energy that we observe today. It then oscillates between $w=-1$ and $1$ with the amplitude of the energy density decaying as $a^{-3}$. If the f…
Current measurements of the low and high redshift Universe are in tension if we restrict ourselves to the standard six parameter model of flat $Λ$CDM. This tension has two parts. First, the Planck satellite data suggest a higher normalization of matter perturbations than local measurements of galaxy clusters. Second, the expansion rate of the Universe today, $H_0$, derived from local distance-redshift measurements is significantly higher than that inferred using the acoustic scale in galaxy surveys and the Planck data as a standard ruler. The addition of a sterile neutrino species changes the …
We construct a simple model of universe with a generalized equation of state $p=(α+kρ^{1/n})ρc^2$ having a linear component $p=αρc^2$ and a polytropic component $p=kρ^{1+1/n}c^2$. For $α=1/3$, $n=1$ and $k=-4/(3ρ_P)$, where $ρ_P=5.16 10^{99} g/m^3$ is the Planck density, this equation of state provides a model of the early universe without singularity describing the transition between the pre-radiation era and the radiation era. The universe starts from $t=-\infty$ but, when $t<0$, its size is less than the Planck length $l_P=1.62 10^{-35} m$. The universe undergoes an inflationary expansion t…
A fundamental assumption inherent in the standard Lambda+CDM Hot Big Bang (HBB) model is that photons lose energy as they are redshifted due to the expansion of the universe. We show that for the Quasi-Static Universe (QSU) model, in which photon energy is an invariant in the cosmological reference frame, the photon number density in the universe today is a factor of approximately 1600 less than in the standard model. We examine some of the consequences for a number of processes that occur during the thermal history of the early universe, including primordial nucleosynthesis, the formation of …
We construct models of universe with a generalized equation of state $p=(αρ+kρ^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider positive indices $n>0$. In that case, the polytropic component dominates in the early universe where the density is high. For $α=1/3$, $n=1$ and $k=-4/(3ρ_P)$, we obtain a model of early universe describing the transition from a pre-radiation era to the radiation era. The universe exists at any time in the past and there is no singularity. However, for $t<0$, its size is less than the Planck length $l_P=1.62 10^{-35} m$. In…
The simple assumption of an instantaneous reionization of the Universe may bias estimates of cosmological parameters. In this paper a model-independent principal component method for the reionization history is applied to give constraints on the cosmological parameters from recent Planck 2015 data. We find that the Universe are not completely reionized at redshifts $z \ge 8.5$ at 95% CL. Both the reionization optical depth and the matter fluctuation amplitude are higher than but consistent with those obtained in the standard instantaneous reionization scheme. The high estimated value of the ma…
The idea that dark matter could be made of stable relics of microscopic black holes is not new. In this article, we revisit this hypothesis, focusing on the creation of black holes by the scattering of trans-Planckian particles in the early Universe. The only new physics required in this approach is an unusually high-energy scale for inflation. We show that dark matter emerges naturally and we study the question of fine-tuning. We finally give some lines of thoughts for a possible detection.
We calculate the Bayesian evidences for a class of Ekpyrotic universe models, and compare with a model of single field inflation with a Higgs-type potential. Combining parsimony and observational constraints, this gives us a systematic way to evaluate the degree to which Ekpyrotic models are constrained by CMB data from Planck. We integrate the equations of motion numerically to define a likelihood using Planck 2018 data and sample this likelihood to obtain Bayesian evidences. Priors are justified and used to put Ekpyrotic models and inflation on equal footing. We find reasonable preference fo…
The question of whether Cosmic Microwave Background (CMB) temperature and polarization data from Planck favor a spatially closed Universe with curvature parameter $Ω_K<0$ has been the subject of recent intense discussions. Attempts to break the geometrical degeneracy combining Planck data with external datasets such as Baryon Acoustic Oscillation (BAO) measurements all point towards a spatially flat Universe, at the cost of significant tensions with Planck, which make the resulting dataset combination problematic. Settling this issue requires identifying a dataset which can break the geometric…
In light of the recent BICEP2 B-mode polarization detection, which implies a large inflationary tensor-to-scalar ratio r_{0.05}=0.2^{+0.07}_{-0.05}, we re-examine the evidence for an extra sterile massive neutrino, originally invoked to account for the tension between the cosmic microwave background (CMB) temperature power spectrum and local measurements of the expansion rate H0 and cosmological structure. With only the standard active neutrinos and power-law scalar spectra, this detection is in tension with the upper limit of r<0.11 (95% confidence) from the lack of a corresponding low multip…
Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh（马拉盖天文与天体物理研究所，马拉盖大学）；Department of Physics, School of Sciences, Ferdowsi University of Mashhad（马什哈德费尔多西大学理学院物理系）；Faculty of Symbiotic Systems Science, Fukushima University（福岛大学共生系统科学学部）
The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and the estimator of gravity $E_G$. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to wea…
We use cosmology-independent measurements of the expansion history in the redshift range 0.1 < z <1.2 and compare them with the Cosmic Microwave Background-derived expansion history predictions. The motivation is to investigate if the tension between the local (cosmology independent) Hubble constant H0 value and the Planck-derived H0 is also present at other redshifts. We conclude that there is no tension between Planck and cosmology independent-measurements of the Hubble parameter H(z) at 0.1 < z < 1.2 for the LCDM model (odds of tension are only 1:15, statistically not significant). Consider…
The effect of the scalar spectral index on inflationary super-Hubble waves is to amplify/damp large wavelengths according to whether the spectrum is red ($n_{s}<1$) or blue ($n_{s}>1$). As a consequence, the large-scale temperature correlation function will unavoidably change sign at some angle if our spectrum is red, while it will always be positive if it is blue. We show that this inflationary filtering property also affects our estimates of the size of the homogeneous patch of the universe through the Grishchuk-Zel'dovich effect. Using the recent quadrupole measurement of ESA's Planck missi…
We consider a model of the early universe which consists of two scalar fields: the inflaton, and a second field which drives the stabilisation of the Planck mass (or gravitational constant). We show that the non-minimal coupling of this second field to the Ricci scalar sources a non-adiabatic pressure perturbation. By performing a fully numerical calculation we find, in turn, that this boosts the amplitude of the primordial power spectrum after inflation.
Starting with geometrical premises, we infer the existence of fundamental cosmological scalar fields. We then consider physically relevant situations in which spacetime metric is induced by one or, in general, by two scalar fields, in accord with the Papapetrou algorithm. The first of these fields, identified with dark energy, has exceedingly small but finite (subquantum) Hubble mass scale (~ 10^-33 eV), and might be represented as a neutral superposition of quasi-static electric fields. The second field is identified with dark matter as an effectively scalar conglomerate composed of primordia…
We present the evolution of dark matter halos in six large cosmological N-body simulations, called the $ν^2$GC (New Numerical Galaxy Catalog) simulations on the basis of the LCDM cosmology consistent with observational results obtained by the Planck satellite. The largest simulation consists of $8192^3$ (550 billion) dark matter particles in a box of $1.12 \, h^{-1} \rm Gpc$ (a mass resolution of $2.20 \times 10^{8} \, h^{-1} M_{\odot}$). Among simulations utilizing boxes larger than $1 \, h^{-1} \rm Gpc$, our simulation yields the highest resolution simulation that has ever been achieved. A $…
We investigate the observational viability of a class of interacting dark energy (iDE) models in the light of the latest Cosmic Microwave Background (CMB), type Ia supernovae (SNe) and SH0ES Hubble parameter measurements. Our analysis explores the assumption of a non-zero spatial curvature, the correlation between the interaction parameter $α$ and the current expansion rate $H_0$, and updates the results reported in \cite{micol}. Initially, assuming a spatially flat universe, the results show that the best-fit of our joint analysis clearly favours a positive interaction, i.e., an energy flux f…
The Cosmic Microwave Background (CMB) is the oldest light in the universe. It is seen today as black body radiation at a near-uniform temperature of 2.73K covering the entire sky. This radiation field is not perfectly uniform, but includes within it temperature anisotropies of order delta(T)/T ~ 10E-5. Physical processes in the early universe have left their fingerprints in these CMB anisotropies, which later grew to become the galaxies and large scale structure we see today. CMB anisotropy observations are thus a key tool for cosmology. The Planck Mission was the European Space Agency's (ESA)…
It is usually assumed that we will need to wait until next-generation surveys like Euclid, LSST and SKA, in order to improve on the current best constraints on primordial non-Gaussianity from the Planck experiment. We show that two contemporary surveys, with the SKA precursor MeerKAT and the Dark Energy Survey (DES), can be combined using the multi-tracer technique to deliver an accuracy on measurement of $f_{\rm NL}$ that is up to three times better than Planck.
We propose a new intuitive metric for evaluating the tension between two experiments, and apply it to several data sets. While our metric is non-optimal, if evidence of tension is detected, this evidence is robust and easy to interpret. Assuming a flat $Λ$CDM cosmological model, we find that there is a modest $2.2σ$ tension between the DES Year 1 results and the ${\it Planck}$ measurements of the Cosmic Microwave Background (CMB). This tension is driven by the difference between the amount of structure observed in the late-time Universe and that predicted from fitting the ${\it Planck}$ data, …
Since the publication of the results of the Planck satellite mission in 2013, the local and early universes have been considered to be in tension in respect of the determination of amplitude of the matter density spatial fluctuations ($σ_8$) and the amount of matter present in the universe ($Ω_m$). This tension can be seen as a lack of massive galaxy clusters in the local universe compared to the prediction inferred from Planck cosmic microwave background (CMB) best-fitting cosmology. In the present analysis, we perform the first detection of the cross-correlation between X-rays and CMB weak-l…
The best-fit values of the density parameter and the amplitude of the linear density power spectrum obtained from the Cosmic Microwave Background (CMB) temperature field scanned by the Planck satellite are found to notably disagree with those estimated from the abundance of galaxy clusters observed in the local universe. Basically, the observed cluster counts are significantly lower than the prediction of the standard flat LambdaCDM model with the key cosmological parameters set at the Planck best-fit values. We show that this inconsistency between the local and the early universe can be well …
This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age. Currently, there are two major methods of independent observational H(z) measurement, which we summarize as the "differential age method" and the "radial BAO size method". Starting with fundamental cosmological notions such as the spacetime coordinates in an expanding universe, we present the basic principles behind the two methods. We further review the two metho…
The first comprehensive analyses of Planck data reveal that the cosmological model with dark energy and cold dark matter can satisfactorily explain the essential physical features of the expanding Universe. However, the inability to simultaneously fit large and small scale TT power spectrum, scalar power index smaller than one and the observations of the violation of the isotropy found by few statistical indicators of the CMB, urge theorists to search for explanations. We show that the model of the Einstein-Cartan cosmology with clustered dark matter halos and their corresponding clustered ang…
In 1914, Planck introduced the concept of a white body. In nature, no true white bodies are known. We assume that the universe after last-scattering is an ideal white body that contains a tremendously large number of thermal photons and is at an extremely high temperature. Bose-Einstein condensation of photons in an ideal white body is investigated within the framework of quantum statistical mechanism. The computation shows that the transition temperature $T_c$ is a monotonically increasing function of the number density $n$ of photons. At finite temperature, we find that the condensate fracti…
The ESA Planck satellite, launched on May 14th, 2009, is the third generation space mission dedicated to the measurement of the Cosmic Microwave Background (CMB), the first light in the Universe. Planck observes the full sky in nine frequency bands from 30 to 857 GHz and is designed to measure the CMB anisotropies with an unprecedented combination of sensitivity, angular resolution and control of systematic effects. In this presentation we summarise the Planck instruments performance and discuss the main scientific results obtained after one year of operations in the fields of galactic and ext…
