We study the matter density fluctuations in the running cosmological constant (RCC) model using linear perturbations in the longitudinal gauge. Using this observable we calculate the growth rate of structures and the matter power spectrum, and compare them with the $SDSS$ data and other available data of the linear growth rate. The distribution of collapsed structures may also constraints models of dark energy. It is shown that RCC model enhances departures from the $ΛCDM$ model for both cluster number and cumulative cluster number predicted. In general increasing the characteristic parameter $ν$ leads to significant growth of the cluster number. In general, we found that the theory of perturbations provides a good tool to distinguish the new model $RCC$ of the standard cosmological model $ΛCDM$.
We present an analysis of the pairwise velocity statistics from a suite of cosmological N-body simulations describing the "Running Friedmann-Lemaître-Robertson-Walker" (R-FLRW) cosmological model. This model is based on quantum field theory in a curved space-time and extends ΛCDM with a time-evolving vacuum energy density. To enforce local conservation of matter a time-evolving gravitational coupling is also included. Our results constitute the first study of velocities in the R-FLRW cosmology, and we also compare with other dark energy simulations suites, repeating the same analysis. We find …
We present a suite of cosmological N-body simulations describing the "Running Friedmann-Lema{ï}tre-Robertson-Walker" (R-FLRW) cosmological model. This model is based on quantum field theory in a curved space-time and extends ΛCDM with a time-evolving vacuum density, Λ(z), and time-evolving gravitational Newton's coupling, G(z). In this paper we review the model and introduce the necessary analytical treatment needed to adapt a reference N-body code. Our resulting simulations represent the first realisation of the full growth history of structure in the R-FLRW cosmology into the non-linear regi…
Bayesian model comparison penalizes models with more free parameters that are allowed to vary over a wide range, and thus offers the most robust method to decide whether some given data require new parameters. In this paper, we ask a simple question: do current cosmological data require extensions of the simplest single-field inflation models? Specifically, we calculate the Bayesian evidence of a totally anti-correlated isocurvature perturbation and a running spectral index of the scalar curvature perturbation. These parameters are motivated by recent claims that the observed temperature aniso…
We investigate the running cosmological constant model with dark energy linearly proportional to the Hubble parameter, $Λ= σH + Λ_0$, in which the $Λ$CDM limit is recovered by taking $σ=0$. We derive the linear perturbation equations of gravity under the Friedmann-Lemaïtre-Robertson-Walker cosmology, and show the power spectra of the CMB temperature and matter density distribution. By using the Markov chain Monte Carlo method, we fit the model to the current observational data and find that $σH_0/ Λ_0 \lesssim 2.63 \times 10^{-2}$ and $6.74 \times 10^{-2}$ for $Λ(t)$ coupled to matter and radi…
We compute the running of the spectrum of cosmological perturbations in String Gas Cosmology, making use of a smooth parametrization of the transition between the early Hagedorn phase and the later radiation phase. We find that the running has the same sign as in simple models of single scalar field inflation. Its magnitude is proportional to $(1 - n_s)$ ($n_s$ being the slope index of the spectrum), and it is thus parametrically larger than for inflationary cosmology, where it is proportional to $(1 - n_s)^2$.
We discussed the dynamics of cosmological models in which the cosmological constant term is a time dependent function through the scale factor $a(t)$, Hubble function $H(t)$, Ricci scalar $R(t)$ and scalar field $ϕ(t)$. We considered five classes of models; two non-covariant parametrization of $Λ$: 1) $Λ(H)$CDM cosmologies where $H(t)$ is the Hubble parameter, 2) $Λ(a)$CDM cosmologies where $a(t)$ is the scale factor, and three covariant parametrization of $Λ$: 3) $Λ(R)$CDM cosmologies, where $R(t)$ is the Ricci scalar, 4) $Λ(ϕ)$-cosmologies with diffusion, 5) $Λ(X)$-cosmologies, where $X=\fra…
It is known than the inclusion of spatial curvature can modify the evolution of matter perturbations and affect the Large Scale Structure (LSS) formation. We quantify the effects of the non-zero space curvature in terms of LSS formation for a cosmological model with a running vacuum energy density and a warm dark matter component. The evolution of density perturbations and the modified shape of its power spectrum are constructed and analyzed.
In light of the most recent cosmological observations, we provide new updated constraints on the slow-roll inflation in different extended scenarios beyond the $Λ\rm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index $α_s$, its running of running $β_s$, the tensor amplitude $r$ and the spatial curvature $Ω_k$. From the Planck 2018 data, we find no evidence for a scalar running or a running of running, while analyzing the Atacama Cosmology Telescope data combine…
The super-horizon second-order density perturbations corresponding to cosmological random fluctuations are considered, their non-vanishing spatial average is shown to be useful in solving the serious problem on the cosmological tension between measured Hubble constants at present and those at the early stage, and the difference from previous works on the backreaction is discussed.
We investigate the power spectra of the CMB temperature and matter density in the running vacuum model (RVM) with the time-dependent cosmological constant of $Λ= 3 νH^2 + Λ_0$, where $H$ is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter $ν$ as well as the cosmological observables. Explicitly, we obtain $ν\leq 1.54 \times 10^{-4}$ (68\% confidence level) in the RVM with the best-fit $χ^2_{\mathrm{RVM}} = 13968.8$, which is slightly smaller than $χ^2_{Λ\math…
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale-dependence, or running, of the density perturbation spectrum. We clarify the…
We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint…
We compute the spectral index of primordial perturbations in a rainbow universe. We allow the Newton constant $G$ to run at (super-)Planckian energies and we consider both vacuum and thermal perturbations. If the rainbow metric is the one associated to a generalized Horava-Lifshitz dispersion relation, we find that only when $G$ tends asymptotically to zero can one match the observed value of the spectral index and solve the horizon problem, both for vacuum and thermal perturbations. For vacuum fluctuations the observational constraints imply that the primordial universe expansion can be both …
Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter sector. For this reason, the phenomenological bounds on such a running are not sufficiently restrictive. The situation can be different in the early universe when the gravitational field was sufficiently strong to provide an efficient creation of particles from the vacuum. We develop a framework for systematically exploring this ossibility. It is su…
We investigate the dynamics of the generalized $Λ$CDM model, which the $Λ$ term is running with the cosmological time. The $Λ(t)$ term emerges from the covariant theory of the scalar field $ϕ$ with the self-interacting potential $V(ϕ)$. On the example of the model $Λ(t)=Λ_{\text{bare}}+\frac{α^2}{t^2}$ we show the existence of a mechanism of the modification of the scaling law for energy density of dark matter: $ρ_{\text{dm}}\propto a^{-3+λ(t)}$. We discuss the evolution of $Λ(t)$ term and pointed out that during the cosmic evolution there is a long phase in which this term is approximately co…
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parametrized as linear functions $Λ(H^2)$ or $Λ(R)$. Such kind of models assume an equation of state for vacuum given by $\,\overline P_Λ=-\,\overlineρ_Λ$, relating their background pressure $\,\overline P_Λ$ and mean energy density $\,\overlineρ_Λ\equivΛ/8πG$. This equation of state requires that the dynamic for vacuum is due to the energy exchange with the material species. Most of the approaches to background level consider only the energy exchange between vacuum and the transient dominant material compon…
In single field slow-roll inflation, one expects that the spectral index $n_s -1$ is first order in slow-roll parameters. Similarly, its running $α_s = dn_s/d \log k$ and the running of the running $β_s = dα_s/d \log k$ are second and third order and therefore expected to be progressively smaller, and usually negative. Hence, such models of inflation are in considerable tension with a recent analysis hinting that $β_s$ may actually be positive, and larger than $α_s$. Motivated by this, in this work we ask the question of what kinds of inflationary models may be useful in achieving such a hiera…
We provide predictions on small-scale cosmological density power spectrum from supernova lensing dispersion. Parameterizing the primordial power spectrum with running $α$ and running of running $β$ of the spectral index, we exclude large positive $α$ and $β$ parameters which induce too large lensing dispersions over current observational upper bound. We ran cosmological N-body simulations of collisionless dark matter particles to investigate non-linear evolution of the primordial power spectrum with positive running parameters. The initial small-scale enhancement of the power spectrum is large…
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…
We investigate the matter density perturbation $δ_m$ and power spectrum $P(k)$ in the running vacuum model (RVM) with the cosmological constant being a function of the Hubble parameter, given by $Λ= Λ_0 + 6 σH H_0+ 3νH^2$, in which the linear and quadratic terms of $H$ would originate from the QCD vacuum condensation and cosmological renormalization group, respectively. Taking the dark energy perturbation into consideration, we derive the evolution equation for $δ_m$ and find a specific scale $d_{cr}=2 π/k_{cr}$, which divides the evolution of the universe into the sub and super-interaction re…
The current vacuum energy density observed as dark energy ${ ρ}_{ \rm dark }\simeq 2.5\times10^{-47}\ {\rm GeV^{4}}$ is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: In terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ${ ρ}_{ \rm vacuum }\simeq m^{2}H^{2}$ where $m$ is the mass of the scalar field and rather dynamical …
Brans-Dicke (BD) cosmology is reconsidered from an approach in which the model can be formulated in $Λ$CDM form, but at the expense of replacing the rigid cosmological constant $Λ$ with a dynamical quasivacuum component which depends on a small parameter $ε$. The product of $ε$ times the BD-parameter $ω_{\rm BD}$ becomes exactly determined in terms of the ordinary cosmological parameters. The GR limit is recovered for $ω_{\rm BD}\to\infty$ when $ε\to 0$. We solve the background cosmology of the model as well as the perturbations equations. When fitted to the cosmological data, we find that the…
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and te…
We present an analysis of the Brans-Dicke cosmological model with a cosmological constant and cold dark matter (BD-$Λ$CDM). We find that the BD-$Λ$CDM is favored by the overall cosmological data (SNIa+BAO+$H(z)$+LSS+CMB) when it is compared with the standard model of cosmology. The BD-$Λ$CDM model can be viewed from the GR perspective as a Running Vacuum Model (RVM) with a time evolving vacuum energy density. Due to this fact and also to its time evolving effective gravitational coupling, the model can alleviate the $σ_8$ and the $H_0$ tensions at a time. We also present the results for differ…
We investigate the cosmological perturbations in the context of a Scalar-Tensor-Vector theory of Gravity known as MOG in the literature. Recent investigations show that MOG reproduces a viable background cosmological evolution comparable to $Λ$CDM. However, the matter-dominated era is slightly different. In this paper, we study the linear matter perturbations and estimate the relevant modified gravity parameters. We show that MOG reduces the growth rate of the perturbations and comparing with the RSD data reveals that MOG suggests a higher value for $σ_8$, compare to $Λ$CDM. This point, consti…
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more b…
We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are shown to be described by a finite number of bases that are gauge invariant. For the second order cosmological perturbations induced by the first order scalar perturbations, we explicitly represent the equations of motion of them in terms of the gauge invariant Newtonian, synchronous and hybrid variables, respectively.
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it is possible to do equivalent analysis in a certain frame in which the perturbation equations are simpler. In this paper we revisit the problem of conformal invariances of cosmological perturbations in terms of the covariant approach in which the perturbation variables have clear geometric and physical meanings. We show that with this approach the conformal in…
We show that a CP-violating interaction induced by a derivative coupling between the running vacuum and a non-conserving baryon current may dynamically break CPT and trigger baryogenesis through an effective chemical potential. By assuming a non-singular class of running vacuum cosmologies which provides a complete cosmic history (from an early inflationary de Sitter stage to the present day quasi-de Sitter acceleration), it is found that an acceptable baryon asymmetry is generated for many different choices of the model parameters. It is interesting that the same ingredient (running vacuum en…
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.
It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $Λ$, which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical conundrum (`the cosmological constant problem') and strongly argue in favor of the possibility that the cosmic vacuum density $ρ_{\rm vac}$ may be mildly evolving with the expansion rate $H$. Such a `running vacuum model' (RVM) proposal predicts an effective dynamical dark energy without postulating new ad hoc fields (quintessence and the like). Using the method of …
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
