In this work, I present for the first time the analysis concerning the growth of matter fluctuations in the framework of $f(R,T)$ modified gravity where I presume $f(R,T) = R + λT$, where $R$ denote the Ricci scalar, $T$ the trace of the energy-momentum tensor and $λ$ a constant. I first solve the Friedman equations assuming a dust universe ($ω=0$) for the Hubble parameter $H(z)$ and then employ it in the equation of matter density fluctuations $δ(z)$ to solve for $δ(z)$ and the growth rate $f(z)$. Next, I proceed to show the behavior of $f(z)$ and $δ(z)$ with redshift for some values of $λ$ with observational constraints. Finally, following the prescription of \cite{growft41}, I present an analytical expression for the growth index $γ$ which is redshift dependent and the expression reduces to $3/5$ for $λ=0$, which is the growth index for a dust universe.
We derive the evolution equation of growth factor for the matter over-dense perturbation in $f(T)$ gravity. For instance, we investigate its behavior in power law model at small redshift and compare it to the prediction of $Λ$CDM and dark energy with the same equation of state in the framework of Einstein general relativity. We find that the perturbation in $f(T)$ gravity grows slower than that in Einstein general relativity if $\p f/\p T>0$ due to the effectively weakened gravity.
In the present paper, we investigate the linear growth of matter fluctuations based on a concrete model of the projected massive gravity, which is free of the Boulware-Deser ghost and preserves the global Lorentz symmetry. We found that at subhorizon scales, the modification to the linear growth is strongly suppressed even without nonlinear screening of an additional force. In addition, we obtain observational constraints from distance and redshift space distortion measurements and find that there is a parameter region that is consistent both observationally and theoretically.
Using redshift space distortion data, we perform model-independent reconstructions of the growth history of matter inhomogeneity in the expanding Universe using two methods: crossing statistics and Gaussian processes. We then reconstruct the corresponding history of the Universe background expansion and fit it to type Ia supernovae data, putting constraints on $(Ω_\mathrm{m,0},σ_{8,0})$. The results obtained are consistent with the concordance flat-$Λ$CDM model and General Relativity as the gravity theory given the current quality of the inhomogeneity growth data.
We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely $f(R)$ gravity and nDGP, and find go…
We re-analyze the nonlocal gravity model of Deser and Woodard which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-$Λ$CDM models can be substantially lower than when its background is fixed by $Λ$CDM. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hints towards a fact that the choice of the backgro…
Adding to our previous method for dealing with gravitational modifications at redshift $z\gtrsim3$ through a single parameter, we investigate treatment of lower redshift modifications to linear growth observables. We establish subpercent accurate fits to the redshift space distortion observable $fσ_8(a)$ using two parameters binned in redshift, testing the results for modifications with time dependence that rises, falls, is nonmonotonic, is multipeaked, and corresponds to $f(R)$ and braneworld gravity. The residuals are then propagated to cosmological parameter biases for DESI observations, an…
We provide for the first time the growth index of linear matter fluctuations of the power law $f(T) \propto (-T)^{b}$ gravity model. We find that the asymptotic form of this particular $f(T)$ model is $γ\approx \frac{6}{11-6b}$ which obviously extends that of the $Λ$CDM model, $γ_Λ\approx 6/11$. Finally, we generalize the growth index analysis of $f(T)$ gravity in the case where $γ$ is allowed to vary with redshift.
We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Eins…
Cosmic growth of large scale structure probes the entire history of cosmic expansion and gravitational coupling. To get a clear picture of the effects of modification of gravity we consider a deviation in the coupling strength (effective Newton's constant) at different redshifts, with different durations and amplitudes. We derive, analytically and numerically, the impact on the growth rate and growth amplitude. Galaxy redshift surveys can measure a product of these through redshift space distortions and we connect the modified gravity to the observable in a way that may provide a useful parame…
Future 21 cm intensity mapping surveys such as SKA can provide precise information on the spatial distribution of the neutral hydrogen (HI) in the post-reionization epoch. This information will allow to test the standard LCDM paradigm and with that the nature of gravity. In this work, we employ the SHYBONE simulations, which model galaxy formation in f(R) modified gravity using the IllustrisTNG model, to study the effects of modified gravity on HI abundance and power spectra. We find that the enhanced growth low-mass dark matter halos experience in f(R) gravity at high redshifts alters the HI …
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…
In this work, we use a combined approach of Hubble parameter data together with redshift-space-distortion $(fσ_8)$ data, which together are used to reconstruct the teleparallel gravity (TG) Lagrangian via Gaussian processes (GP). The adopted Hubble data mainly comes from cosmic chronometers, while for the Type Ia supernovae data we use the latest jointly calibrated Pantheon compilation. Moreover, we consider two main GP covariance functions, namely the squared-exponential and Cauchy kernels in order to show consistency (to within 1$σ$ uncertainties). The core results of this work are the numer…
Constraining Scale-Dependent Growth in $f(R)$ Gravity with Future 21 cm Surveys
Indian Institute of Technology Mandi（印度理工学院曼迪分校）；University of Cape Town（开普敦大学）；North-West University（西北大学）；South African Astronomical Observatory（南非天文台）；Duy Tan University（Duy 坦大学）
We consider a homogeneous and isotropic Universe, described by the minisuperspace Lagrangian with the scale factor as a generalized coordinate. We show that the energy of a closed Universe is zero. We apply the uncertainty principle to this Lagrangian and propose that the quantum uncertainty of the scale factor causes the primordial fluctuations of the matter density. We use the dynamics of the early Universe in the Einstein$-$Cartan theory of gravity with spin and torsion, which eliminates the big-bang singularity and replaces it with a nonsingular bounce. Quantum particle production in highl…
About 70\% of the Universe is Dark Energy, but the physics community still does not know what it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. Previously, we studied the Universe's accelerated expansion, where DG was able to explain the SNe-Ia data successfully. In this work, we explore the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculate the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing…
We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), CMB (WMAP7), weak lensing (CFHTLS) and peculiar velocity of galaxies (WiggleZ). We fit modified gravity parameters of the generalized Poisson equations simultaneously with the effective equation of state for the background evolution, exploring the covariances and model dependence. The results show that general relativity is a good fit to the combined data. Using a Pad{é} approximant form for the gravity deviations accurately captures the time an…
The quantum fluctuation of the stress tensor of a quantum field are discussed, as are the resulting spacetime metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the spacetime geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.
A probability of distinguishing between $Λ$CDM model and modified gravity is studied by using the future observations for the growth rate of cosmic structure (Euclid redshift survey). Adopting extended DGP model, Kinetic Gravity Braiding model, and Galileon model as modified gravity, we compare predicted cosmic growth rate by models to the mock observational data. The growth rate $fσ_8$ in the original DGP model is suppressed compared with the $Λ$CDM case, for the same value of the current density parameter of matter $Ω_{m,0}$, because of the suppression of effective gravitational constant. In…
In this paper, we study the growth index of matter density perturbations for the power law model in $f(T)$ gravity. Using the parametrization $γ(z)=γ_0+γ_1 {z\over 1+z}$ for the growth index, which approximates the real evolution of $γ(z)$ very well, and the observational data of the growth factor, we find that, at $1σ$ confidence level, the power law model in $f(T)$ gravity is consistent with the observations, since the obtained theoretical values of $γ_0$ and $γ_1$ are in the allowed region.
We present the first steps needed for an analysis of the perturbations that occur in the cosmology associated with the conformal gravity theory. We discuss the implications of conformal invariance for perturbative coordinate gauge choices, and show that in the conformal theory the trace of the metric fluctuation kinematically decouples from the first-order gravitational fluctuation equations. We determine the equations that describe first-order metric fluctuations around the illustrative conformally flat de Sitter background. Via a conformal transformation we show that such fluctuations can be…
The article reviews the current state of the field, and also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations, active gravity noise cancellation, and time-domain models of gravity perturbations from atmospheric and seismic point sources. Our understanding of terrestrial gravity fluctuations will have great impact on the future development of GW detectors and high-precision gravimetry in general, and many open questions need to be answered still as emphasized in this article.
In this paper we study the evolution of density perturbations in the framework of Phase Coupling Gravity theory at the very early universe. We show that these perturbation display an exponential-like behaviour.
The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black holes within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in $f(R)$ gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.
We re-examine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable "rainbow frame" this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal…
An exact de Sitter solution of scalar-tensor gravity is found, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown in this article.
In this paper we study gauge-invariant metric fluctuations from a Noncompact Kaluza-Klein (NKK) theory of gravity in a de Sitter expansion. We recover the well known result $δρ/ρ\simeq 2Φ$, obtained from the standard 4D semiclassical approach to inflation. The spectrum for these fluctuations should be dependent of the fifth (spatial-like) coordinate.
The growth of matter perturbations in the $f(R)$ model proposed by Starobinsky is studied in this paper. Three different parametric forms of the growth index are considered respectively and constraints on the model are obtained at both the $1σ$ and $2σ$ confidence levels, by using the current observational data for the growth factor. It is found, for all the three parametric forms of the growth index examined, that the Starobinsky model is consistent with the observations only at the $2σ$ confidence level.
We study background dynamics and the growth of matter perturbations in the extended quasidilaton setup of massive gravity. For the analysis of perturbations, we first choose a scalar field matter component and obtain the conditions under which all scalar perturbations are stable. We work in unitary gauge for the matter field, which allows us to directly map to known results in the limit of general relativity. By performing a parameter search, we find that the perturbations are unstable in general, while a particular choice of potential, where the scalar field effectively behaves like pressurel…
The Einstein-Langevin equation is a perturbative correction to the semiclassical Einstein equation which takes into account the lowest order quantum fluctuations of the matter stress-energy tensor. It predicts classical stochastic fluctuations in the metric field which may describe some of the remnant gravitational fluctuations after the process of environment induced decoherence driving the quantum to classical transition of gravity.
In this work, we shall analyze the effects of quantum fluctuations on the properties of a BTZ black hole, in a massive theory of gravity. We will analyze this for a charged BTZ black hole in asymptotically AdS and dS space-times. The quantum fluctuations would produce thermal fluctuations in the thermodynamics of this BTZ black hole. As these fluctuations would become relevant at a sufficiently small scale, we shall discuss the effects of such thermal fluctuations on the entropy of a small charged BTZ black. We shall also analyze the effects of these fluctuations on the stability of such a bla…
We investigate the potential of cosmological observations, such as galaxy surveys, for constraining degenerate higher-order scalar-tensor (DHOST) theories, focusing in particular on the linear growth of the matter density fluctuations. We develop a formalism to describe the evolution of the matter density fluctuations during the matter dominated era and in the early stage of the dark energy dominated era in DHOST theories, and give an approximate expression for the gravitational growth index in terms of several parameters characterizing the theory and the background solution under consideratio…
We show how the quantum potential arises in various ways and trace its connection to quantum fluctuations and Fisher information along with its realization in terms of Weyl curvature. It is a quantization factor for certain classical systems as well as an expression for quantum matter in gravity theories of Weyl-Dirac type. We extract theories and examples from the literature, providing connections and interpretations, and make a few new observations.
We study slow-roll inflation and the generation of primordial fluctuations in $F(T)$ gravity's rainbow. We obtain the second order action for scalar and tensor perturbations and then calculate the primordial power spectrum for them. Thus, after calculating the inflationary observables up to first order in slow-roll approximation, namely the scalar spectral index $n_{s}$ and the tensor-to scalar ratio $r$, we confront the predictions of the model with the current PLANCK and BICEP/Keck data.
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a non-scale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both…
We study the complexity growth by using complexity = action (CA) proposal in Minimal Massive 3D Gravity(MMG) model which is proposed for resolving the bulk-boundary clash problem of Topologically Massive Gravity(TMG). We observe that the rate of the complexity growth for BTZ black hole saturates the proposed bound by physical mass of the BTZ black hole in the MMG model, when the angular momentum parameter and the inner horizon of black hole goes to zero.
Stochastic semiclassical gravity is a theory for the interaction of gravity with quantum matter fields which goes beyond the semiclassical limit. The theory predicts stochastic fluctuations of the classical gravitational field induced by the quantum fluctuations of the stress energy tensor of the matter fields. Here we use an axiomatic approach to introduce the Einstein-Langevin equations as the consistent set of dynamical equations for a first order perturbative correction to semiclassical gravity and review their main features. We then describe the application of the theory in a simple chaot…
To study the effect of parity-violation on the rate of complexity growth, by using "Complexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter $μ$, which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and…
Recently, a novel Einstein-Gauss-Bonnet gravity in four dimensions has been introduced [Phys. Rev. Lett. 124 (2020) 081301]. We will investigate cosmological consequences of this model in details. We will consider linear matter density perturbations and also estimate relevant modified gravity parameters. Specially we will concentrate on the growth rate of non-relativistic matter perturbations on top of FRW geometry and show that for a narrow range of the Gauss-Bonnet coupling constant, observational data will be satisfied. In this paper, it is shown that for enough large values of the coupling…
We examine tensor perturbations around a deSitter background within the framework of Ashtekar's variables and cousins parameterized by the Immirzi parameter $γ$. At the classical level we recover standard cosmological perturbation theory, with illuminating insights. Quantization leads to real novelties. In the low energy limit we find a second quantized theory of gravitons which displays different vacuum fluctuations for right and left gravitons. Nonetheless right and left gravitons have the same (positive) energies, resolving a number of paradoxes suggested in the literature. The right-left a…
We study fluctuations and correlations between spacial regions, generated by the primordial quantum gravitational phase of the universe. We do so by a numerical evaluation of Lorentzian amplitudes in Loop Quantum Gravity, in a non-semiclassical regime. We find that the expectation value of the quantum state of the geometry emerging from the early quantum phase of the universe is a homogeneous space but fluctuations are very large and correlations are strong, although not maximal. In particular, this suggests that early quantum gravitational effects could be sufficient to solve the cosmological…
We propose a thought experiment to detect low-energy Quantum Gravity phenomena using Quantum Optical Information Technologies. Gravitational field perturbations, such as gravitational waves and quantum gravity fluctuations, decohere the entangled photon pairs, revealing the presence of gravitational field fluctuations including those more speculative sources such as compact extra dimensions and the sub-millimetric hypothetical low-energy quantum gravity phenomena and then set a limit for the decoherence of photon bunches and entangled pairs in space detectable with the current astronomical spa…
We compare observational data of growth rate with the prediction by Galileon theory. For the same value of the energy density parameter $Ω_{m,0}$, the growth rate in Galileon models is enhanced compared with the $Λ$CDM case, due to the enhancement of Newton's constant. The smaller $Ω_{m,0}$ is, the more suppressed growth rate is. Hence the best fit value of $Ω_{m,0}$ in the Galileon model is 0.16 from only the growth rate data, which is considerably smaller than such value obtained from observations of supernovae Ia, the cosmic microwave background and baryon acoustic oscillations. This result…
The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by t…
We introduce gravity theories featuring spontaneously growing gauge fields where the growth is due to the Higgs mechanism. The underlying physics is inspired by the spontaneous scalarization phenomena in scalar-tensor theories. The tachyonic instability that causes the growth in spontaneous scalarization and its analog for vector fields is introduced not as an explicit potential term, but through a scalar coupling using a Higgs field. The resulting theories are distinct from previous examples of spontaneous tensorization in that they respect the gauge symmetry at the level of the action. Our r…
A single parameter, the gravitational growth index γ, succeeds in characterizing the growth of density perturbations in the linear regime separately from the effects of the cosmic expansion. The parameter is restricted to a very narrow range for models of dark energy obeying the laws of general relativity but takes on distinctly different values in models of beyond-Einstein gravity. In analogy to the parameterized post-Newtonian (PPN) formalism for testing gravity, we extend and motivate the gravitational growth index, or Minimal Modified Gravity, approach to parameterizing beyond-Einstein cos…
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.
A correspondence between fluctuations of conformally invariant quantum fields and that of classical fields finally reducing to perfect fluid matter content is shown to exist. Previously a similar correspondence between the stress tensors was known and well established in the 70's. Using recent results obtained in semiclassical stochastic gravity regarding exact definition and significance given to quantum fluctuations of the stress tensor, we obtain this correspondence, which is fundamental to statistical analysis of systems in curved spacetime. This is of immense importance, in that the fluct…
The observability of primordial cosmic fluctuations does not require a geometric horizon $H^{-1}$, which is exceeded temporarily by the wavelength of fluctuations. The primordial information can be protected against later thermal washout even if all relevant wavelengths remain smaller than $H^{-1}$. This is demonstrated by formulating the equations governing the cosmic fluctuations in a form that is manifestly invariant under conformal field transformations of the metric. Beyond the field equations this holds for the defining equation for the correlation function, as expressed by the inverse o…
We investigate the growth factor for sub-horizon modes during late times in $f(T,\mathcal{T})$ gravity, where $T$ is the torsion scalar and $\mathcal{T}$ is the trace of the stress-energy tensor. This is achieved by obtaining the modified Mészáros equation, which describes the evolution of the perturbations of the matter energy density, and obtaining numerical results. Such results are obtained by solving the modified continuity equation and analysing the behaviour of the solutions of the latter using various constraints on the integration constants. Furthermore, the role of the anisotropic te…
The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.
In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a …
The standard field-theoretical approach to the slow-roll inflation is introduced. We then show as, in order to calculate the mean square of the canonical gauge invariant quantum fluctuations associated to a generic field, the logarithm of the scale factor has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. Then we compute the growth of different test fields with a small effective mass during slow-roll inflationary models, comparing the results with the one for the gauge invariant canonical fluctuation associated to the inflaton, the Mukhanov variable. …
The present work is related to anisotropic cosmological evolution in metric $f(R)$ theory of gravity. The initial part of the paper develops the general cosmological dynamics of homogeneous anisotropic Bianchi-I spacetime in $f(R)$ cosmology. The anisotropic spacetime is pervaded by a barotropic fluid which has isotropic pressure. The paper predicts nonlinear growth of anisotropy in such spacetimes. In the later part of the paper we display the predictive power of the nonlinear differential equation responsible for the cosmological anisotropy growth in various relevant cases. We present the ex…
We introduce a cosmological model in the framework of Generalised Massive Gravity. This theory is an extension of non-linear massive gravity with a broken translation symmetry in the Stückelberg space. In a recent work, we showed the existence of cosmological solutions stable against linear perturbations. In the present paper, we build up on the previous result and study the evolution of the background solutions and the linear perturbations. At the background level, we find that the mass terms act like a fluid with time dependent equation of state $w < -1$ at late times. At linear order, we de…
We examine the thermodynamics of a regular charged black hole (RCB) added with corrections due to massive gravity and thermal fluctuations at quantum level. We then derive the expressions for all the relevant thermodynamic quantities such as entropy, Hawkings temperature, internal energy, Gibbs free energy, corrected to first order. We also briefly discuss the stability of such a system with the help of quantities like specific heat and thermodynamic pressure, along with this we present their comparative study with the corresponding original values.
We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which took place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass $ \propto H^2$ (with $H$ as the Hubble parameter) and a massless non-minimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean…
