We study the effects of modified theories of gravity on the cosmic microwave background (CMB) anisotropies power spectrum, and in particular on its large scales, where the integrated Sachs-Wolfe (ISW) effect is important. Starting with a general parametrisation, we then specialise to f(R) theories and theories with Yukawa-type interactions between dark matter particles. In these models, the evolution of the metric potentials is altered, and the contribution to the ISW effect can differ significantly from that in the standard model of cosmology. We proceed to compare these predictions with observational data for the CMB and the ISW, performing a full Monte Carlo Markov chain (MCMC) analysis. In the case of f(R) theories, the result is an upper limit on the lengthscale associated to the extra scalar degree of freedom characterising these theories. With the addition of data from the Hubble diagram of Type Ia supernovae, we obtain an upper limit on the lengthscale of the theory of B_0 < 0.4, or correspondingly λ_1 < 1900 Mpc/h at 95% c.l. improving previous CMB constraints. For Yukawa-type models we get a bound on the coupling 0.75 < β_1 < 1.25 at the 95% c.l. We also discuss the implications of the assumed priors on the estimation of modified gravity parameters, showing that a marginally less conservative choice improves the f(R) constraints to λ_1 < 1400 Mpc/h, corresponding to B_0 < 0.2 at 95% c.l.
We forecast the constraints on modified theories of gravity from the cosmic microwave background (CMB) anisotropies bispectrum that arises from correlations between lensing and the Integrated Sachs-Wolfe effect. In models of modified gravity the evolution of the metric potentials is generally altered and the contribution to the CMB bispectrum signal can differ significantly from the one expected in the standard cosmological model.We adopt a parametrised approach and focus on three different classes of models: Linder's growth index, Chameleon-type models and f(R) theories. We show that the cons…
Model-independent parametrisations for examining departures from General Relativity have been increasingly studied over the past few years. Various observables have been used to constrain the parameters and forecasts for future surveys have been carried out. In one such forecast, galaxy cluster counts were used to constrain the parameters. Here, we carry out a limited set of $N$-body simulations, with a modified Poisson equation, to examine the accuracy of existing mass functions for modified gravity cosmologies. As well as altering the gravitational calculation, we include the effect of a scr…
We present $\texttt{MG-evolution}$, an $N$-body code simulating the cosmological structure formation for parametrised modifications of gravity. It is built from the combination of parametrised linear theory with a parametrisation of the deeply nonlinear cosmological regime extrapolated from modified spherical collapse computations that cover the range of known screening mechanisms. We test $\texttt {MG-evolution}$, which runs at the speed of conventional $Λ$CDM simulations, against a suit of existing exact model-specific codes, encompassing linearised and chameleon $f(R)$ gravity as well as th…
In a modified gravity theory, the propagation equation of gravitational waves will be presented in a non-standard way. Therefore this tenor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique character distinguishing modified gravity from general relativity. To avoid the model-dependent issue, in this paper, we propose a parametrised modification to the propagation of gravitational waves. We show the effects on the angular power spectrum of cosmic microwave background radiation due to the parametrised modification and its degeneracy to the tensor…
Cosmological structures grow differently in theories of gravity which are modified as compared to Einstein's General relativity (GR). Cosmic microwave background (CMB) fluctuation patterns at the last scattering surface are lensed by these structures along the photon path to the observer. The observed CMB pattern therefore keeps trace of the growth history of structures. We show that observations of the CMB lensing bi-spectrum offer an interesting way to constrain deviations from GR in a broad class of scalar-tensor theories of gravity called "beyond Horndeski". We quantify how the constraints…
We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of ISW-Lensing bispectrum and CMB power spectrum. We find that, even considering the temperature-temperature mode of CMB power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with WMAP. T…
In modified gravity theories, the gravitational waves propagation are presented in nonstandard ways. We consider a friction term different from GR and constrain the modified gravitational waves propagation from observations. The modified gravitational waves produce anisotropies and polarization which generate measurable tensor power spectra. We explore the impact of the friction term on the power spectrum of B-modes and the impact on the constraints on the other parameters (e.g., $r$ or $A_t$) when $ν_0$ is allowed to vary in the Monte Carlo analyses from Planck+BK18 datasets. If we assume the…
The observed discrepancy of the Hubble parameter measurements in the local universe with the cosmic microwave background (CMB) data may indicate a new physics. It is vital to test the alternative models that reconcile the Hubble tension with other cosmological observations in this direction. The CMB lensing is a crucial observation that relates the early universe perturbations to the matter's late-time distribution. In this work, we study the prediction of the ü$Λ$CDM as a solution for $H_0$ tension for CMB lensing and the low- and high-$\ell$'s temperature (TT) power spectrum internal inconsi…
No Slip Gravity is a simple modified gravity theory with only one free function and the interesting characteristic that -- unlike many modified gravity theories -- it suppresses growth. This allows it to fit current redshift space distortion and $σ_8$ mass fluctuation amplitude data better than $Λ$CDM in general relativity, while retaining a $Λ$CDM background expansion and hence distances. Since it has no gravitational slip it alters equally CMB lensing and matter density growth, and in addition affects the CMB gravitational wave B-mode polarization power spectrum. We investigate and compute t…
We use the optimised skew-spectrum as well as the skew-spectra associated with the Minkowski Functionals (MFs) to test the possibility of using the cross-correlation of the Integrated Sachs-Wolfe effect (ISW) and lensing of the cosmic microwave background (CMB) radiation to detect deviations in the theory of gravity away from General Relativity (GR). We find that the although both statistics can put constraints on modified gravity, the optimised skew-spectra are especially sensitive to the parameter $\rm B_0$ that denotes the the {\em Compton wavelength} of the scalaron at the present epoch. W…
Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppre…
Observational cosmology has become an important laboratory for testing General Relativity, with searches for modified gravity forming a significant portion of the science case for existing and future surveys. In this paper, we illustrate how future measurements of the Cosmic Microwave Background (CMB) temperature and polarization anisotropies can be combined with large galaxy surveys to improve constraints on modified gravity using the technique of Sunyaev Zel'dovich (SZ) tomography. SZ tomography uses the correlations between the kinetic/polarized SZ contributions to the small-angular scale C…
We consider the effect of modified gravity on the peak structure of the Cosmic Microwave Background (CMB) spectrum. We focus on simple models of modified gravity mediated by a massive scalar field coupled to both baryons and cold dark matter. This captures the features of chameleon, symmetron, dilaton and $f(R)$ models. We find that the CMB peaks can be affected in three independent ways provided the Compton radius of the massive scalar is not far-off the sound horizon at last scattering. When the coupling of the massive scalar to Cold Dark Matter (CDM) is large, the anomalous growth of the CD…
Planck-2015 data seem to favour a large value of the lensing amplitude parameter, $A_{\rm L}=1.22\pm0.10$, in CMB spectra. This result is in $2σ$ tension with the lensing reconstruction result, $A_{\rm L}^{ϕϕ}=0.95\pm0.04$. In this paper, we simulate several CMB anisotropy and CMB lensing spectra based on Planck-2015 best-fit cosmological parameter values and Planck blue book beam and noise specifications. We analyse several modified gravity models within the effective field theory framework against these simulations and find that models whose effective Newton constant is enhanced can modulate…
We examine general physical parameterisations for viable gravitational models in the $f(R)$ framework. This is related to the mass of an additional scalar field, called the scalaron, that is introduced by the theories. Using a simple parameterisation for the scalaron mass $M(a)$ we show there is an exact correspondence between the model and popular parameterisations of the modified Poisson equation $μ(a,k)$ and the ratio of the Newtonian potentials $η(a,k)$. However, by comparing the aforementioned model against other viable scalaron theories we highlight that the common form of $μ(a,k)$ and $…
We use the cross-correlation power spectrum of the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropy and galaxy fluctuations to probe the physics of late-time cosmic acceleration. For this purpose, we focus on three models of dark energy that belong to a sub-class of Horndeski theories with the speed of gravity equivalent to that of light: Galileon Ghost Condensate (GGC), Generalized Cubic Covariant Galileon (GCCG), and K-mouflage. In the GGC and GCCG models, the existence of cubic-order scalar self-interactions allows a possibility for realizi…
Weak gravitational lensing leaves a characteristic imprint on the cosmic microwave background temperature and polarization angular power spectra. Here we investigate the possible constraints on the integrated lensing potential from future CMB angular spectra measurements expected from Planck and EPIC. We find that Planck and EPIC will constrain the amplitude of the integrated projected potential responsible for lensing at 6% and 1% level, respectively with very little sensitivity to the shape of the lensing potential. We discuss the implications of such a measurement in constraining dark energ…
The dispersion relation of graviton is a fundamental issue for fundamental physics about gravity. In this paper we investigate how the modified dispersion relation of graviton affects the cosmic microwave background (CMB) power spectra, in particular the B-mode polarization. Our results will be useful to test the dispersion relation of graviton at the energy scale around $10^{-29}$ eV.
We present a new method for delensing $B$ modes of the cosmic microwave background (CMB) using a lensing potential reconstructed from the same realization of the CMB polarization (CMB internal delensing). The $B$-mode delensing is required to improve sensitivity to primary $B$ modes generated by, e.g., the inflationary gravitational waves, axion-like particles, modified gravity, primordial magnetic fields, and topological defects such as cosmic strings. However, the CMB internal delensing suffers from substantial biases due to correlations between observed CMB maps to be delensed and that used…
The $Λ$CDM concordance model is very successful at describing our Universe with high accuracy and few parameters. Despite its successes, a few tensions persist; most notably, the best-fit $Λ$CDM model, as derived from the Planck CMB data, largely overpredicts the abundance of SZ clusters when using their standard mass calibration. Whether this is a sign of an incorrect calibration or the need for new physics remains a matter of debate. Here we examined two simple extensions of the standard model and their ability to release this tension: massive neutrinos and a simple modified gravity model vi…
We show that, in the presence of massive neutrinos, the Galileon gravity model provides a very good fit to the current CMB temperature, CMB lensing and BAO data. This model, which we dub $ν \rm{Galileon}$, when assuming its stable attractor background solution, contains the same set of free parameters as $Λ\rm{CDM}$, although it leads to different expansion dynamics and nontrivial gravitational interactions. The data provide compelling evidence ($\gtrsim 6σ$) for nonzero neutrino masses, with $Σm_ν\gtrsim 0.4\ {\rm eV}$ at the $2σ$ level. Upcoming precision terrestrial measurements of the abso…
We discuss the phenomenological imprints of modifications to gravity in the early universe with a specific focus on the time of recombination. We derive several interesting results regarding the effect that such modifications have on cosmological observables, especially on the driving and phasing of acoustic oscillations, observed in the CMB and BAO, as well as the weak gravitational lensing of the CMB and of galaxy shapes. This widens the pool of measurements that can be used to test gravity with present and future surveys, in particular realizing the full constraining power of the structure …
Effects of velocity dispersion of dark matter particles on the CMB TT power spectrum and on the matter linear power spectrum are investigated using a modified CAMB code. Cold dark matter originated from thermal equilibrium processes does not produce appreciable effects but this is not the case if particles have a non-thermal origin. A cut-off in the matter power spectrum at small scales, similar to that produced by warm dark matter or that produced in the late forming dark matter scenario, appears as a consequence of velocity dispersion effects, which act as a pressure perturbation.
Gravity-induced non-Gaussianity can provide important clues to Modified Gravity (MG) Theories. Several recent studies have suggested using the {\it Integrated Bispectrum} (IB) as a probe for squeezed configuration of bispectrum. Extending previous studies on the IB, we include redshift-space distortions to study a class of (parametrised) MG theories that include the string-inspired Dvali, Gabadadze \& Porrati (DGP) model. Various contributions from redshift-space distortions are derived in a transparent manner, and squeezed contributions from these terms are derived separately. Results are obt…
Cosmic microwave background polarization encodes information not only on the early universe but also dark energy, neutrino mass, and gravity in the late universe through CMB lensing. Ground based surveys such as ACTpol, PolarBear, SPTpol significantly complement cosmological constraints from the Planck satellite, strengthening the CMB dark energy figure of merit and neutrino mass constraints by factors of 3-4. This changes the dark energy probe landscape. We evaluate the state of knowledge in 2017 from ongoing experiments including dark energy surveys (supernovae, weak lensing, galaxy clusteri…
In this paper, we quantify the ability of a future measurement of the Sandage-Loeb test signal from the Cosmic-Dynamic-Experiment-like spectrograph to constrain some popular modified gravity theories including DGP brane-world scenario, $f(R)$ modified gravity and $f(T)$ gravity theory. We find that the Sandage-Loeb test measurements are able to break degeneracies between model parameters markedly and thus greatly improve cosmological constraints for all concerned modified gravity theories when combined with the latest observations of CMB--shift parameter. However, they yield almost the same de…
Cosmological gravity on all scales V: MCMC forecasts combining large scale structure and CMB lensing for binned phenomenological modified gravity
Ludwig-Maximilians Universität（路德维希-马克西米利安大学）；Indian Instititute for Science Education and Research (IISER)（印度科学教育研究所）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）；Excellence Cluster ORIGINS（ORIGINS卓越集群）；University of Sussex（萨塞克斯大学）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理研究所）
Lensing of the Cosmic Microwave Background (CMB) changes the morphology of pattern of temperature fluctuations, so topological descriptors such as Minkowski Functionals can probe the gravity model responsible for the lensing. We show how the recently introduced two-to-two and three-to-one kurt-spectra (and their associated correlation functions), which depend on the power spectrum of the lensing potential, can be used to probe modified gravity theories such as $f({R})$ theories of gravity and quintessence models. We also investigate models based on effective field theory, which include the con…
Deviations from the standard $Λ$CDM model motivate an interpretation of early universe cosmology using the Scalar-Tensor-Vector-Gravity (STVG) theory. A constraint analysis carried out by Valentino, Melchiorri and Silk, revealed deviations from the growth of structure predicted by General Relativity, and a lensing anomaly in the angular CMB power spectrum data. The modified gravity (MOG) theory resolves the lensing deviation from the standard model and provides an explanation of the CMB and structure growth data.
We investigate the Minimal Theory of Massive Gravity (MTMG) in the light of different observational data sets which are in tension within the $Λ$CDM cosmology. In particular, we analyze MTMG model, for the first time, with the Planck-CMB data, and how these precise measurements affect the free parameters of the theory. The MTMG model can affect the CMB power spectrum at large angular scales and cause a suppression on the amplitude of the matter power spectrum. We find that on adding Planck-CMB data, the graviton has a small, positive, but non-zero mass at 68\% confidence level, and from this p…
We study the effects of Lorentz symmetry violation on the scalar CMBR bispectrum. Our quantitative results show that there can be enhancements in the bispectrum for specific configurations in momentum space, when the modified dispersion relations resulting from the symmetry breaking violate the adiabatic condition for a short period of time in the early Universe. The kind of configurations that are enhanced and the pattern of oscillations in wavenumbers that generically appear in the bispectrum strictly depend on the form of the modified dispersion relation, and therefore on the pattern of Lor…
Inspired by quantum gravitational physics, the approach of non-commutative (NC) phase space leads to a modified dispersion relation of gravitational waves. This feature, if applied to the very early universe, gives rise to a modified power spectrum of primordial tensor perturbations with a suppression of power on large scales. We confront this phenomenon with the BICEP2 and Planck experiments, and show that inflation with the modified dispersion relation can simultaneously fit the observations better than the standard inflationary paradigm. In particular, the numerical result implies that with…
An important piece of evidence for dark matter is the need to explain the growth of structure from the time of horizon entry and radiation-matter equality to the formation of stars and galaxies. This cannot be explained by using general relativity without dark matter. So far, dark matter particles have not been detected in laboratory measurements or at the LHC. We demonstrate that enhanced structure growth can happen in a modified gravity theory (MOG). The vector field and particle introduced in the theory to explain galaxy and cluster dynamics plays an important role in generating the require…
Cosmic microwave background radiation can supply us some most significant parts of the information on the universe. Some researchers believe that The gravitational system cannot be decribed by the standard statistical mechanics. In this article we apply Tsallis nonextensive statistical mechanics to investigate CMB spectrum and related cosmological processes. Based on recent observational data we find that the nonextensive statistical mechanics can modify the values of related physical quantites. Since the value of physical quantites have changed, some processes, such as recombination, can be a…
Model-independent parametrisations of modified gravity have attracted a lot of attention over the past few years; numerous combinations of experiments and observables have been suggested to constrain these parameterisations, and future surveys look very promising. Galaxy Clusters have been mentioned, but not looked at as extensively in the literature as some other probes. Here we look at adding Galaxy Clusters into the mix of observables and examine whether they could improve the constraints on the modified gravity parameters. In particular, we forecast the constraints from combining the Planc…
The observed acceleration of the universe, explained through dark energy, could alternatively be explained through a modification of gravity that would also induce modifications in the evolution of cosmological perturbations. We use new weak lensing data from the COSMOS survey to test for deviations from General Relativity. The departure from GR is parametrized in a model-independent way that consistently parametrizes the two-point cosmic shear amplitude and growth. Using CMB priors, we perform a likelihood analysis. We find constraints on the amplitude of the signal that do not indicate a dev…
We have succeeded in establishing a cosmological model with a non-minimally coupled scalar field $ϕ$ that can account not only for the spatial periodicity or the picket-fence structure exhibited by the galaxy $N$-$z$ relation of the 2dF survey, but also for the spatial power spectrum of the cosmic microwave background radiation (CMB) temperature anisotropy observed by the WMAP satellite. The scalar field of our model universe starts from an extremely small value at around the nucleosynthesis epoch, remains in that state for sufficiently long periods, allowing sufficient time for the CMB temper…
We study the formation of voids in a modified gravity model in which gravity is generically stronger or weaker on large scales. We show that void abundances provide complementary information to halo abundances: if normalized to the CMB, models with weaker large-scale gravity have smaller large scale power, fewer massive halos and fewer large voids, although the scalings are not completely degenerate with $σ_8$. Our results suggest that, in addition to their abundances, halo and void density profiles may also provide interesting constraints on such models: stronger large scale gravity produces …
The fundamental properties of the photon have deep impact on the astrophysical processes that involve it, like the inverse Compton scattering of CMB photon by energetic electrons residing within galaxy cluster atmospheres, usually referred to as the Sunyaev-Zel'dovich effect (SZE). We calculate the combined constraints on the photon decay time and mass by studying the impact of the modified CMB spectrum, as recently calculated (Heeck 2013), on the SZE of galaxy clusters. We analyze the modifications of the SZE as produced by photon decay effects. We study in details the frequency regimes where…
Model-independent parametrisations of modified gravity have attracted a lot of attention over the past few years and numerous combinations of experiments and observables have been suggested to constrain the parameters used in these models. Galaxy clusters have been mentioned, but not looked at as extensively in the literature as some other probes. Here we look at adding galaxy clusters into the mix of observables and examine how they could improve the constraints on the modified gravity parameters. In particular, we forecast the constraints from combining Planck satellite Cosmic Microwave Back…
In this paper we study cosmological signatures of modified gravity theories that can be written as a coupling between a extra scalar field and the electromagnetic part of the usual Lagrangian for the matter fields. In these frameworks all the electromagnetic sector of the theory is affected and variations of fundamental constants, of the cosmic distance duality relation and of the evolution law of the cosmic microwave background radiation (CMB) are expected and are related each other. In order to search these variations we perform jointly analyses with angular diameter distances of galaxy clus…
The existence of the inflationary era in the early Universe seems to be strongly supported by recent CMB observations. However, only a few realistic inflation scenarios which have close relation to particle physics seem to have been known unfortunately. The radiative neutrino mass model with inert doublet dark matter is a promising model for the present experimental issues which cannot be explained within the standard model. In order to make the model include inflation, we extend it by a complex scalar field with a specific potential. This scalar could be closely related to the neutrino mass g…
We study in this paper three different theories of gravitation with massive gravitons - the modified Fierz-Pauli (FP) model, Massive Gravity and the bimetric theory proposed by Visser - in linear perturbation theory around a Minkowski and a flat FRW background. For the TT tensor perturbations we show that the three theories give rise to the same dynamical equations and to the same form of the Boltzmann equations for the radiative transfer in General Relativity (GR). We then analyze vector perturbations in these theories and show that they do not give the same results as in the previous case. W…
The precision measurements of the cosmic microwave background power spectrum put a strong constraint on the dark matter annihilation cross section since the electromagnetic energy injection by the dark matter annihilation affects the ionization history of the universe. In this paper, we update our previous simulation code for calculating the ionization history with the effect of dark matter annihilation by including Helium interactions and improving the precision of calculations. We give an updated constraint on the annihilation cross section and mass of dark matter using the modified RECFAST …
The cosmic microwave background (CMB) is sensitive to the recent phase of accelerated cosmic expansion through the late-time integrated Sachs-Wolfe (ISW) effect, which manifests as secondary temperature fluctuations on large angular scales. However, the large cosmic variance from primary CMB fluctuations limits the usefulness of this effect in constraining dark energy or modified gravity. In this paper, we propose a novel method to separate the ISW signal from the primary signal using gravitational lensing, based on the fact that the ISW signal is, to a good approximation, not gravitationally …
