Semiclassical contributions to the gravitational action include various terms with zero, two, and four derivatives of the metric as well as nonlocal form factors for these terms. Contributions to some of these terms could be confused with others on a specific metric background or for a particular gauge fixing. We present a critical analysis of the recent works where the tensor structure and the number of derivatives in the action of gravity were not properly taken into account. Taking these relevant aspects into account, we show that although some contributions owing to the quantum fluctuations of massive or massless scalar as well as fermion and vector fields may be attributed to the "running" of the cosmological constant, in reality they correspond to the fourth derivative terms of the action.
We consider cosmological properties of modified gravity with nonlocal term $ R^p\mathcal{F}(\Box)R^q$ in its Lagrangian. Equations of motion are presented. For the flat FLRW metric, and some particular values of natural numbers $p$ and $q$ cosmological solutions of the form $a(t)= C e^{- \frac γ{12}t^2}$ are found.
We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem in a de Sitter and Anti-de Sitter background. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. A canonical decomposition of modes is used to separate transverse-traceless tensors (graviton) from ghosts and scalar. We show that no ghosts appear in the final evaluation of the cosmological constant. A zeta function regularization is used to handle with divergences. A re…
We compute the running of the cosmological constant and Newton's constant taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive the cosmological constant to zero.
In this paper, we suggest that the early universe starts from a high-energetic state with a two dimensional description and the state recovers to be four dimensional when the universe evolves into the radiation dominated phase. This scenario is consistent with the recent viewpoint that quantum gravity should be effectively two dimensional in the ultraviolet and recovers to be four dimensional in the infrared. A relationship has been established between the running of effective dimension and that of the entropy inside particle horizon of the universe, i.e., as the effective dimension runs from …
We consider some cosmological aspects of nonlocal modified gravity with $Λ$ term, where nonlocality is of the type $R \mathcal{F}(\Box) R$. Using ansatz of the form $\Box R = r R +s,$ we find a few a(t) nonsingular bounce cosmological solutions for all three values of spatial curvature parameter k. We also discuss this modified gravity model from F(R) theory point of view.
On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of the cosmological constant today, (ii) the evolution of the universe from an inflationary era after the big-bang till now, and (iii) local supersymmetry in the gravitational sector (supergravity) with a broken spectrum at early eras, by making use of the concept of the "running vacuum" in the context of a simple toy model of four-dimensional N=1 supergravity. …
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.
We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of p…
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 briefly review the previous works on the renormalization group in quantum general relativity with the cosmological constant, based on the Vilkovisky and DeWitt version of effective action. On top of that, we discuss the prospects of the applications of this version of renormalization group to the cosmological models with a running Newton constant and vacuum energy density.
Current astronomical observations are successfully explained by the present cosmological paradigm based on the concordance model ($Λ_0$CDM + Inflation). However, such a scenario is composed of a heterogeneous mix of ingredients for describing the different stages of cosmological evolution. Particularly, it does not give an unified explanation connecting the early and late time accelerating inflationary regimes which are separated by many aeons. Other challenges to the concordance model include: a singularity at early times or the emergence of the Universe from the quantum gravity regime, the "…
Renormalization group (RG) improved cosmologies based upon a RG trajectory of Quantum Einstein Gravity (QEG) with realistic parameter values are investigated using a system of cosmological evolution equations which allows for an unrestricted energy exchange between the vacuum and the matter sector. It is demonstrated that the scale dependence of the gravitational parameters, the cosmological constant in particular, leads to an entropy production in the matter system. The picture emerges that the Universe started out from a state of vanishing entropy, and that the radiation entropy observed tod…
We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the non-local effective action and effective field equation methods. In all cases we fin…
In the recent literature on dark energy (DE) model building we have learnt that cosmologies with variable cosmological parameters can mimic more traditional DE pictures exclusively based on scalar fields (e.g. quintessence and phantom). In a previous work we have illustrated this situation within the context of a renormalization group running cosmological term, Lambda. Here we analyze the possibility that both the cosmological term and the gravitational coupling, G, are running parameters within a more general framework (a variant of the so-called ``LXCDM models'') in which the DE fluid can be…
This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with $Λ$ term, we introduce nonlocality by the following way: $R - 2 Λ= \sqrt{R-2Λ}\ \sqrt{R-2Λ} \to \sqrt{R-2Λ}\ F(\Box)\ \sqrt{R-2Λ} ,$ where ${F} (\Box) = 1 + \sum_{n= 1}^{+\infty} \big( f_n \Box^n + f_{-n} \Box^{-n} \big) $ is an analytic function of the d'Alembert-Beltrami operator $\Box$ and its inverse $\Box^{-1}$. By this way, $R$ and $Λ$ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator $F(\Box)$…
We study the renormalisation group running of the cosmological and the Newton constant, where the renormalisation scale is given by the inverse of the radius of the cosmological event horizon. In this framework, we discuss the future evolution of the universe, where we find stable de Sitter solutions, but also "big crunch"-like and "big rip"-like events, depending on the choice of the parameters in the model.
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \emph{commutative} manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter fields are utilized to generate self-consistent Abelian Drinfeld twists in a background independent manner and their continuous and discrete symmetries are examined. There is negligible experimental effect on the standard model of particles. While baryonic twist producing matter would begin to behave acausally for rest masses above $\sim1-10$ TeV, other poss…
Employing an effective field theory approach to inflationary perturbations, we analyze in detail the effect of curvature-generated Lagrangian operators on various observables, focusing on their running with scales. At quadratic order, we solve the equation of motion at next-to-leading leading order in a generalized slow-roll approximation for a very general theory of single-field inflation. We derive the resulting power spectrum, its tilt and running. We then focus on the contribution to the primordial non-Gaussianity amplitude f_{NL} sourced by a specific interaction term. We show that the ru…
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-NUT-AdS/dS spacetimes.
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…
In this work we investigate the renormalization group flow of the cosmological constant $Λ$ induced by the change in space-time curvature in the electroweak vacuum. We calculate the generic magnitude resulting from running in the standard model in a subtraction scheme that respects the Appelquist-Carazzone decoupling theorem. Interestingly, we find in this prescription that for a non-minimal coupling $ξ\lesssim 10^4$ the magnitude of the generated contribution remains below the value consistent with observations.
For a generic quantum field theory we study the role played by the renormalization-group (RG) running of the cosmological constant (CC) in determining the ultimate fate of the universe. We consider the running of the CC of generic origin (the vacuum energy of quantum fields and the potential energy of classical fields), with the RG scale proportional to the (total energy density$\rm{)^{1/4}}$ as the most obvious identification. Starting from the present-era values for cosmological parameters we demonstrate how the running can easily provide a negative cosmological constant, thereby changing th…
We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is non perturbative and contains a condensate of the metric tensor in a manner reminiscent of Yang-Mills theories. As a simple step toward the characterization of such a vacuum the value of the one-loop effective action is computed for Euclidean de Sitter spaces as a function of the curvature when the unstable conformal modes are held fixed. Two phases are found, one where the curvature is large and gravitons should be confined and another one which appears to be weakly coupled and tends to be flat. Th…
We present the connection between the running of the cosmological constant and the estimate of its value in the resummed quantum gravity realization of quantum general relativity. We also address in this way some of the questions that have been raised concerning this latter generalization and application of the original prescription of Feynman for the formulation of quantum general relativity.
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…
A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this paper is twofold. First, we find that box-counting dimension in face…
We establish an indirect link between relic neutrinos and the dark energy sector which originates from the vacuum energy contributions of the neutrino quantum fields. Via renormalization group effects they induce a running of the cosmological constant with time which dynamically influences the evolution of the cosmic neutrino background. We demonstrate that the resulting reduction of the relic neutrino abundance allows to largely evade current cosmological neutrino mass bounds and discuss how the scenario might be probed by the help of future large scale structure surveys and Planck data.
In this paper, we explore an idea of having Newton's constant change its value depending on the curvature scale involved. Such modification leads to a particular scalar-tensor gravity theory, with the Lagrangian derived from renormalization group (RG) flow arguments. Several of the well-known f(R) modified gravity models have remarkably simple description in terms of the infrared renormalization group, but not the "designer" types in general. We find that de Sitter-like accelerated expansion can be generated even in the absence of cosmological constant term, entirely due to running of the Newt…
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…
During hundred years of General Relativity (GR), many significant gravitational phenomena have been predicted and discovered. General Relativity is still the best theory of gravity. Nevertheless, some (quantum) theoretical and (astrophysical and cosmological) phenomenological difficulties of modern gravity have been motivation to search more general theory of gravity than GR. As a result, many modifications of GR have been considered. One of promising recent investigations is Nonlocal Modified Gravity. In this article we present a brief review of some nonlocal gravity models with their cosmolo…
Within the Quantum Field Theory context the idea of a "cosmological constant" (CC) evolving with time looks quite natural as it just reflects the change of the vacuum energy with the typical energy of the universe. In the particular frame of Ref.[30], a "running CC" at low energies may arise from generic quantum effects near the Planck scale, M_P, provided there is a smooth decoupling of all massive particles below M_P. In this work we further develop the cosmological consequences of a "running CC" by addressing the accelerated evolution of the universe within that model. The rate of change of…
Despite the many outstanding cosmological observations leading to a strong evidence for a nonvanishing cosmological constant (CC) term in the gravitational field equations, the theoretical status of this quantity seems to be lagging well behind the observational successes. It thus seems timely to revisit some fundamental aspects of the CC term in Quantum Field Theory (QFT). We emphasize that, in curved space-time, nothing a priori prevents this term from potentially having a mild running behavior associated to quantum effects. Remarkably, this could be the very origin of the dynamical nature o…
Asymptotically safe quantum gravity predicts running gravitational and cosmological constants, while it remains a meaningful quantum field theory because of the existence of non-Gaussian ultraviolet fixed points. Here we have investigated the effect of such running couplings on the cosmological perturbations. We have obtained the improved Mukhanov-Sassaki equation and solved it for two models. The effect of asymptotically safe quantum gravity on the cosmological power spectrum is also studied.
The idea of a variable dark energy has been entertained many times in the literature and from many different points of view. Quintessence is just a popular way to implement this idea in recent times, but so far with little success. Another possibility is to think of the cosmological term, Lambda, as a ``running quantity'' much in the same way as the electromagnetic coupling constant. However, the fact that Lambda is a dimension-four parameter implies that it may obey a peculiar renormalization group equation, which at low energies could be dominated by ``soft decoupling'' contributions of the …
We extend the adiabatic regularization method by introducing an arbitrary mass scale $μ$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $μ$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has…
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…
Starting from generic quantum effects at the Planck scale M_P, we find that the renormalization group running of the cosmological constant (CC) at low energies is possible if there is a smooth decoupling of all massive particles from M_P to the mass of the lightest neutrino. We discuss the theoretical implications of this running for the ``old'' and ``new'' cosmological constant problems. Interestingly enough, the CC running implies a strong relationship between quantum field theory and cosmology, which should be observable in the near future in experiments such as SNAP through the measurement…
In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/Ricci flow models with nontrivial torsion to configurations with the Levi-Civita connection is allowed in some specific physical circumstances by constraining the class of integral varieties for the Eins…
In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the ``cosmological constant'' is not a constant in a quantum field theory context, still less should be zero. In this paper we continue with previous work, and derive the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time. At higher energies the calculation is performed in a sharp cut off approximation. We assess, in two different frameworks, whether the scaling dependences of the …
Nonlocal gravity has been shown to provide a phenomenologically viable infrared modification of GR. A natural question is whether the required nonlocality can emerge from perturbative quantum loop corrections due to light particles. We show that this is not the case. For the value of the mass scale of the non-local models required by cosmology, the perturbative form factors obtained from the loop corrections, in the present cosmological epoch, are in the regime where they are local. The mechanism behind the generation of the required nonlocality must be more complex, possibly related to strong…
Using standard quantum field theory, we discuss several theoretical aspects of the possible running of the cosmological constant (CC) term in Einstein's equations. The basic motivation for the present work is to emphasize that this possibility should also be taken into account when considering dynamical models for the dark energy (DE), which are nowadays mainly focused on identifying the DE with the energy density associated to one or more ad hoc scalar fields. At the same time, we address some recent criticisms that have been published (or privately communicated to us) attempting to cast doub…
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…
We study asymptotically safe gravity with Einstein-Hilbert truncation taking into account the renormalization group running of both gravitational and cosmological constants. We show the classical behavior of the theory is equivalent to a specific class of Jordan-Brans-Dicke theories with vanishing Brans-Dicke parameter, and potential determined by the renormalization group equation. The theory may be reformulated as an $f(R)$ theory. In the simplest cosmological scenario, we find large--field inflationary solutions near the Planck scale where the effective field theory description breaks down.…
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 suggest that the (small but nonvanishing) cosmological constant, and the holographic properties of gravitational entropy, may both reflect unconventional quantum spin-statistics at a fundamental level. This conjecture is motivated by the nonlocality of quantum gravity and the fact that spin is an inherent property of spacetime. As an illustration we consider the `quon' model which interpolates between fermi and bose statistics, and show that this can naturally lead to an arbitrarily small cosmological constant. In addition to laboratory tests, we briefly discuss the possible observable impr…
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…
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…
In this paper we put forward a running coupling scenario for describing the interaction between dark energy and dark matter. The dark sector interaction in our scenario is free of the assumption that the interaction term $Q$ is proportional to the Hubble expansion rate and the energy densities of dark sectors. We only use a time-variable coupling $b(a)$ (with $a$ the scale factor of the universe) to characterize the interaction $Q$. We propose a parametrization form for the running coupling $b(a)=b_0a+b_e(1-a)$ in which the early-time coupling is given by a constant $b_e$, while today the coup…
The idea of the quantum state of the Universe described by some density matrix, i.e mixture of at least two vacua, the trivial symmetric and the nontrivial one with spontaneously broken symmetry is discussed. Nonzero cosmological constant necessarily arises for such a state and has the observable value if one takes the axion mass for the vacuum expectation value. The Higgs model, Nambu's model and discrete symmetry breaking are considered. Human observers can observe only the world on the nonsymmetric vacuum, the world on the other vacuum is some dark matter. Gravity is due to action of two wo…
