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Ozgur Akarsu

Publications and source records attributed to Ozgur Akarsu.

At least 19 recordsLinked to original sources

Updated Constraints on Omnipotent Dark Energy: A Comprehensive Analysis with CMB and BAO Data

In this work, we present updated observational constraints on the parameter space of the DMS20 dark energy model, a member of the omnipotent dark energy (ODE) class. Our analysis combines multiple CMB datasets - including measurements from the Planck satellite (PL18), the South Pole Telescope (SPT), and the Wilkinson Microwave Anisotropy Probe (WMAP) - with Type Ia supernova data from the Pantheon$+$ catalog (PP), and baryon acoustic oscillation (BAO) measurements from the DESI and SDSS surveys. We find that certain data combinations, such as SPT+WMAP+BAO and PL18+BAO, can reduce the significance of the $H_0$ tension below $1σ$, but with considerably large uncertainties. However, the inclusion of PP data restores the tension in $H_0$. To provide a comprehensive view of the ODE phenomenology, we also investigate the evolution of its energy density, emphasizing its dynamical behavior at low redshifts. Our results generically exhibit multiple phantom divide line crossings in a single expansion history; if confirmed, this points beyond the simplest minimally coupled canonical single-field quintessence/phantom descriptions and motivates more general dark-sector realizations.

gr-qc

Quadratic energy-momentum squared gravity: constraints from big bang nucleosynthesis

In this work, we extend the standard cosmological model within the quadratic energy-momentum squared gravity (qEMSG) framework, introducing a nonminimal interaction between the usual material field ($T_{μν}$) and its accompanying partner field (qEMSF, $T_{μν}^{\rm qEMSF}$), defined by $f(\mathbf{T}^2)=α\mathbf{T}^2$ with $\mathbf{T^2}=T_{μν}T^{μν}$. Adopting an analytical approach within the qEMSG framework, we present a comprehensive exploration of Big Bang Nucleosynthesis (BBN) dynamics. Our analysis selects the radiation-dominated universe solution compatible with the standard cosmological model limit as $α\rightarrow0$ and reveals that qEMSF interaction model can modify the radiation energy density's evolution, potentially altering neutron-proton interconversion rates and consequently affecting $^4$He abundance in various ways. By explicitly defining modifications to the predicted primordial $^4$He mass fraction, $Y_{\rm p}$, we establish the most stringent cosmological constraints on the parameter $α$ based on recent measurements of $Y_{\rm p}$: $(-8.81\leqα\leq8.14)\times10^{-27}\,\mathrm{eV}^{-4}$ (68% CL) from Aver et al.'s primordial $^4$He abundance measurements, aligning with $α=0$. Additionally, $(3.48\leqα\leq4.43)\,\times 10^{-27}\rm{eV}^{-4}$ (68% CL) from Fields et al.'s estimates, utilizing the Planck-CMB estimated baryon density within the standard cosmological model framework, diverges from $α=0$, thereby lending support to the qEMSF interaction model. The study also highlights the bidirectional nature of energy-momentum/entropy transfer in qEMSF interaction model, depending on the sign of $α$. The implications of qEMSF in the presence of additional relativistic relics are also explored, showcasing the model's potential to accommodate deviations from standard cosmology and the Standard Model of particle physics.

astro-ph.CO

Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density

While $f(T)$ gravity has shown considerable potential in addressing cosmological tensions, we explore previously overlooked solution spaces that hold further promise. We examine the case where the customary assumption of a strictly positive effective DE density may not apply, offering new possibilities. Focusing on $f(T) = T e^{T_*/T}$, we investigate cosmological solutions parametrized by the parameter $β= T_*/T_0$. This parameter uniquely determines $Ω_{\rm m0}$, and its sign plays a crucial role in characterizing deviations from the $Λ$CDM. We elaborate on the structural asymmetry between the positive- and negative-$β$ branches: while the $β_{+}$ leads to dynamics with modest departures from $Λ$CDM, the $β_{-}$ yields more pronounced and nontrivial deviations. Despite these deviations, the negative-$β$ branch can remain consistent with local gravity constraints through an effective chameleon-like mechanism. We also examine the model in the context of dynamical DE. Ensuring consistency with CMB data, the widely studied $β_{+}$ exhibits phantom behavior, while the previously overlooked $β_{-}$ features a sign-changing DE density that transitions smoothly from negative to positive values at $z_{\dagger} \sim 1.5$. Though the sign-changing DE leads to a larger-than-expected enhancement, we extend the analysis by incorporating $Λ$. This extension broadens the solution space consistent with the SH0ES measurement while maintaining consistency with CMB. Additionally, it introduces richer phenomenological possibilities, including the potential moderation or cessation of cosmic acceleration at very low redshifts, aligning with recent observational analyses, such as those from DESI BAO data. Our findings suggest that existing $f(T)$ models, as well as $f(Q)$ models, should be revisited in light of the novel theoretical insights presented here.

gr-qc

$Λ_{\rm s}$CDM cosmology: Alleviating major cosmological tensions by predicting standard neutrino properties

We investigate a two-parameter extension of the $Λ_{\rm s}$CDM model by allowing variations in the effective number of neutrino species $N_{\rm eff}$ and their total mass $\sum m_ν$. Our motivation is twofold: (i) to examine whether $Λ_{\rm s}$CDM retains its success in fitting the data and addressing major cosmological tensions, without suggesting a need for a deviation from the standard model of particle physics, and (ii) to determine whether the data indicate new physics that could potentially address cosmological tensions, either in the post-recombination universe through the late-time mirror AdS-dS transition, or in the pre-recombination universe through modifications in the standard values of $N_{\rm eff}$ and $\sum m_ν$, or both. Within the extended $Λ_{\rm s}$CDM model, referred to as $Λ_{\rm s}$CDM+$N_{\rm eff}$+$\sum m_{\rm ν}$, we find no significant tension when considering the Planck-alone analysis. We observe that incorporating BAO data limits the further success of the $Λ_{\rm s}$CDM extension. However, the weakly model-dependent BAOtr data, along with Planck and Planck+PP\&SH0ES, favor $H_0\sim 73\,{\rm km\, s^{-1}\, Mpc^{-1}}$. In cases where BAOtr dataset is used, the mirror AdS-dS transition is very effective in providing enhanced $H_0$ values, and thus the model requires no significant deviation from the standard value of $N_{\rm eff} = 3.044$. Both the $H_0$ and $S_8$ tensions are effectively addressed, with some compromise in the case of the Planck+BAO dataset. Finally, the upper bounds obtained on $\sum m_ν\lesssim 0.5$~eV are fully compatible with neutrino oscillation experiments. Our findings provide evidence that late-time physics beyond $Λ$CDM, such as $Λ_{\rm s}$CDM, without altering the standard pre-recombination universe, can suffice to alleviate the major cosmological tensions.

astro-ph.CO

Transition dynamics in the $Λ_{\rm s}$CDM model: Implications for bound cosmic structures

We explore the predictions of $Λ_{\rm s}$CDM, a novel framework suggesting a rapid anti-de Sitter (AdS) to de Sitter (dS) vacua transition in the late Universe, on bound cosmic structures. In its simplest version, the cosmological constant, $Λ_{\rm s}$, abruptly switches sign from negative to positive, attaining its present-day value at a redshift of ${z_\dagger\sim 2}$. The $Λ_{\rm s}$CDM model emerges as a promising solution to major cosmological tensions, particularly the $H_0$ and $S_8$ tensions, as well as other less definite tensions. A key aspect of our investigation is examining the impact of the abrupt $Λ_{\rm s}$CDM model on the formation and evolution of bound cosmic structures. We identify three primary influences: (i) the negative cosmological constant (AdS) phase for $z > z_\dagger$, (ii) the abrupt transition marked by a type II (sudden) singularity, leading to an abrupt increase in the universe's expansion rate at $z=z_\dagger$, and (iii) an increased expansion rate in the late universe under a positive cosmological constant for $z < z_\dagger$, compared to $Λ$CDM. Utilizing the spherical collapse model, we investigate the non-linear evolution of bound cosmic structures within the $Λ_{\rm s}$CDM framework. We find that the virialization process of cosmic structures, and consequently their matter overdensity, varies depending on whether the AdS-dS transition precedes or follows the turnaround. Specifically, structures virialize with either increased or reduced matter overdensity compared to the Planck-$Λ$CDM model, contingent on the timing of the transition. Additionally, our results demonstrate that the sudden singularity does not result in the dissociation of bound systems. Despite its profound nature, the singularity exerts only relatively weak effects on such systems, thereby reinforcing the model's viability in this context.

astro-ph.CO

Omnipotent dark energy: A phenomenological answer to the Hubble tension

This paper introduces the class of omnipotent dark energy (DE) models characterized by nonmonotonic energy densities that are capable of attaining negative values with corresponding equation of state parameters featuring phantom divide line (PDL) crossings and singularities. These nontrivial features are phenomenologically motivated by findings of previous studies that reconstruct cosmological functions from observations, and the success of extensions of $Λ$CDM, whose actual or effective DE density is omnipotent, in alleviating the observational discordance within $Λ$CDM. As an example, we focus on one embodiment of omnipotent DE, viz., the DE parametrization introduced in Di Valentino et al. [Dark energy with phantom crossing and the H0 tension, Entropy 23, 404 (2021)] (DMS20). By updating and extending the datasets used in the original paper where it was introduced, we confirm the effectiveness of DMS20 in alleviating the observational discrepancies. Additionally, we uncover that its negative DE density feature, importance of which was not previously investigated, plays a crucial role in alleviating the tensions, along with the PDL crossing feature that the parametrization presupposes. In particular, we find that there is a positive correlation between the $H_0$ parameter and the scale ($a_p$) at which DE density transitions from negative to positive, in agreement with previous studies that incorporate this transition feature. For our full dataset, the model yields $H_0=70.05 \pm 0.64$ (68% CL) relaxing the $H_0$ tension with a preference of crossing to negative DE densities ($a_p>0$ at 99% CL), along with the constraint $a_m=0.922^{+0.041}_{-0.035}$ on the scale of the presupposed PDL crossing.

astro-ph.CO

Model-independent reconstruction of the Interacting Dark Energy Kernel: Binned and Gaussian process

The cosmological dark sector remains an enigma, offering numerous possibilities for exploration. One particularly intriguing option is the (non-minimal) interaction scenario between dark matter and dark energy. In this paper, to investigate this scenario, we have implemented Binned and Gaussian model-independent reconstructions for the interaction kernel alongside the equation of state; while using data from BAOs, Pantheon+ and Cosmic Chronometers. In addition to the reconstruction process, we conducted a model selection to analyze how our methodology performed against the standard $Λ$CDM model. The results revealed a slight indication, of at least 1$σ$ confidence level, for some oscillatory dynamics in the interaction kernel and, as a by-product, also in the DE and DM. A consequence of this outcome is the possibility of a sign change in the direction of the energy transfer between DE and DM and a possible transition from a negative DE energy density in early-times to a positive one at late-times. While our reconstructions provided a better fit to the data compared to the standard model, the Bayesian Evidence showed an intrinsic penalization due to the extra degrees of freedom. Nevertheless these reconstructions could be used as a basis for other physical models with lower complexity but similar behavior.

astro-ph.CO

$\mathbb{T}^{2}$- inflation: Sourced by energy-momentum squared gravity

In this paper, we examine chaotic inflation within the context of the energy-momentum squared gravity (EMSG) focusing on the energy-momentum powered gravity (EMPG) that incorporates the functional $f(\mathbb{T}^2)\propto (\mathbb{T}^2)^β$ in the Einstein-Hilbert action, in which $β$ is a constant and $\mathbb{T}^2\equiv T_{μν}T^{μν}$ where $T_{μν}$ is the energy-momentum tensor, which we consider to represent a single scalar field with a power-law potential. We demonstrate that the presence of EMSG terms allows the single-field monomial chaotic inflationary models to fall within current observational constraints, which are otherwise disfavored by Planck and BICEP/Keck findings. We show that the use of a non-canonical Lagrangian with chaotic potential in EMSG can lead to significantly larger values of the non-Gaussianity parameter, $f_{\rm Nl}^{\rm equi}$ whereas EMSG framework with canonical Lagrangian gives rise to results similar to those of the standard single-field model.

gr-qc

Weak field and slow motion limits in energy-momentum powered gravity

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy-momentum powered gravity (EMPG), viz., the energy-momentum squared gravity (EMSG) of the form $f(T_{μν}T^{μν})=α(T_{μν}T^{μν})^η$ with $α$ and $η$ being constants. We have shown that EMPG with $η\geq0$ and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, $M_{\rm ast}$, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass $M_{\rm eff}(α,η,M)=M+M_{\rm empg}(α,η,M)$, $M$ being the actual physical mass and $M_{\rm empg}$ being the modification due to EMPG. Accordingly, while in GR we simply have the relation $M_{\rm ast}=M$, in EMPG we have $M_{\rm ast}=M+M_{\rm empg}$. Within the framework of EMPG, if there is information about the values of $\{α,η\}$ pair or $M$ from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only $M_{\rm ast}$ alone from astronomical observations, but $M$ and $M_{\rm empg}$ separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by $|p_{\rm eff}/ρ_{\rm eff}|\ll1$ (where $p_{\rm eff}=p+p_{\rm empg}$ and $ρ_{\rm eff}=ρ+ρ_{\rm empg}$), whereas this condition leads to $|p/ρ|\ll1$ in GR.

gr-qc

$Λ_{\rm s}$CDM model: A promising scenario for alleviation of cosmological tensions

We present a comprehensive analysis of the $Λ_{\rm s}$CDM model, which explores the recent conjecture suggesting a rapid transition of the Universe from anti-de Sitter vacua to de Sitter vacua (viz., the cosmological constant switches sign from negative to positive) at redshift ${z_\dagger\sim 2}$, inspired by the graduated dark energy (gDE) model. Our analysis shows that, predicting $z_\dagger\approx1.7$, $Λ_{\rm s}$CDM simultaneously addresses the major cosmological tensions of the standard $Λ$CDM model, viz., the Hubble constant $H_0$, the Type Ia Supernovae absolute magnitude $M_{\rm B}$, and the growth parameter $S_8$ tensions, along with other less significant tensions such as the BAO Lyman-$α$ discrepancy.

astro-ph.CO

Relaxing cosmological tensions with a sign switching cosmological constant: Improved results with Planck, BAO, and Pantheon data

We present a further observational analysis of the $Λ_{\rm s}$CDM model proposed in Akarsu et al. [Phys. Rev. D 104, 123512 (2021)]. This model is based on the recent conjecture suggesting the Universe has transitioned from anti-de Sitter vacua to de Sitter vacua (viz., the cosmological constant switches sign from negative to positive), at redshift ${z_\dagger\sim2}$, inspired by the graduated dark energy model proposed in Akarsu et al. [Phys. Rev. D 101, 063528 (2020)]. $Λ_{\rm s}$CDM was previously claimed to simultaneously relax five cosmological discrepancies, namely, the $H_0$, $S_8$, and $M_B$ tensions along with the Ly-$α$ and $ω_{\rm b}$ anomalies, which prevail within the standard $Λ$CDM model as well as its canonical/simple extensions. In the present work, we extend the previous analysis by constraining the model using the Pantheon data (with and without the SH0ES $M_B$ prior) and/or the completed BAO data along with the full Planck CMB data. We find that $Λ_{\rm s}$CDM exhibits a better fit to the data compared to $Λ$CDM, and simultaneously relaxes the six discrepancies of $Λ$CDM, viz., the $H_0$, $M_B$, $S_8$, Ly-$α$, $t_0$, and $ω_{\rm b}$ discrepancies, all of which are discussed in detail. When the $M_B$ prior is included in the analyses, $Λ_{\rm s}$CDM performs significantly better in relaxing the $H_0$, $M_B$, and $S_8$ tensions with the constraint ${z_\dagger\sim1.8}$ even when the Ly-$α$ data (which imposed the $z_\dagger\sim2$ constraint in the previous studies) are excluded. In contrast, the presence of the $M_B$ prior causes only negligible improvements for $Λ$CDM. Thus, the $Λ_{\rm s}$CDM model provides remedy to various cosmological tensions simultaneously, only that the galaxy BAO data hinder its success to some extent.

astro-ph.CO

Inevitable manifestation of wiggles in the expansion of the late Universe

Using the fact that the comoving angular diameter distance to the last scattering surface is strictly constrained almost model independently, we show that, for any model agreeing with the standard $Λ$CDM model on its background dynamics at $z\sim0$ and size of the comoving sound horizon at last scattering, the deviations of the Hubble radius from the one of the standard $Λ$CDM model must be a member of the set of admissible wavelets. The family of models characterized by this framework also offers nontrivial oscillatory behaviours in various functions that define the kinematics of the Universe, even when the wavelets themselves are very simple. We also discuss the consequences of attributing these kinematics to, first, dark energy, and second, varying gravitational coupling strength. Utilizing some simplest wavelets, we demonstrate the competence of this framework in describing the baryon acoustic oscillation (BAO) data without any modifications to the agreement with cosmic microwave background measurements. This framework also provides a natural explanation for the bumps found in nonparametric observational reconstructions of the Hubble parameter and dark energy density as compensations of the dips suggested by some BAO data, and questions the physical reality of their existence. We note that utilizing this framework on top of the models that agree with both the cosmic microwave background and local $H_0$ measurements but are held back by BAO data, one may resurrect these models through the wiggly nature of wavelets that can naturally accommodate the BAO data. Finally, we also suggest narrowing the plausible set of admissible wavelets to further improve our framework by imposing conditions from expected kinematics of a viable cosmological model or first principle fundamental physics such as energy conditions.

astro-ph.CO

Relativistic binary systems in scale-independent energy-momentum squared gravity

In this paper, we study the gravitational-wave (GW) radiation and radiative behavior of relativistic binary systems in the scale-independent energy-momentum squared gravity (EMSG). Using the post-Minkowskian gravity based on the Landau-Lifshitz formulation of the theory, the field equations of the scale-independent EMSG are solved approximately. The gravitational potential in the wave zone of a gravitational source is then obtained. Doing so, we derive the GW signals emitted from a binary system. The results are different from those obtained in general relativity (GR). It is shown that the relevant non-GR corrections modify the wave amplitude and leave the GW polarizations unchanged. In this case, the system loses energy to modified GWs. This leads to a change in the secular variation of the Keplerian parameters of the binary system. In this work, we investigate the non-GR effects on the radiative parameter, i.e., the first time derivative of the orbital period. Next, applying these results together with GW observations from the relativistic binary systems, we constrain/test the scale-independent EMSG theory in the strong-field regime. After assuming that GR is the valid gravity theory, as a priori expectation, we find that the free parameter of the theory is of the order $10^{-5}$ from the direct GW observation, the GW events GW190425 and GW170817, as well as the indirect GW observation, the double pulsar PSR J0737$-$3039A/B experiment.

gr-qc

Cosmological models in scale-independent energy-momentum squared gravity

Scale-independent EMSG is a particular model of energy-momentum squared gravity (EMSG) in which the new terms in the Einstein field equations arising from the EMSG theory enter with the same power as the usual terms from Einstein-Hilbert part of the action. However, the model violates the local energy-momentum conservation and matter-current conservation in general and hence, permits a process of matter creation/annihilation in an expanding universe. Consequently, the scale factor dependencies of the energy densities are modified by the dimensionless model parameter $α$. We revisit some nostalgias such as static universes and de Sitter/steady state universes. We reproduce the original ones, moreover, present some novelties, e.g., a spatially flat static universe, de Sitter expansion by negative vacuum energy, steady state universes in the presence of arbitrary fluids with constant equation of state (EoS) parameter other than dust, etc. We also investigate the possible dynamics of dust dominated and radiation dominated universes. Depending on the value of $α$, dust/radiation dominated universe exhibits power-law accelerated/decelerated expansion, corresponds to a steady state model or may end in a big rip. In the framework of anisotropic cosmology, we reproduce Barrow's quiescent universe in the presence of stiff fluid and extend it to fluids with arbitrary constant EoS parameter. We also relax the condition for isotropic initial singularity (big bang) owing to that EMSG effectively allows ultra-stiff EoS parameters.

gr-qc

Testing spatial curvature and anisotropic expansion on top of the $Λ$CDM model

We explore the possible advantages of extending the $Λ$CDM model by more realistic backgrounds compared to its spatially flat RW spacetime assumption, while preserving the underpinning physics; in particular, by simultaneously allowing non-zero spatial curvature and anisotropic expansion on top of it, viz., the An-$oΛ$CDM model. This is to test whether the latest data support spatial flatness and/or isotropic expansion, and, if not, to explore the roles of spatial curvature and expansion anisotropy (due to its stiff fluid-like behavior) in addressing some of the cosmological tensions. We first present the theoretical background and explicit mathematical construction of An-$oΛ$CDM; combining the simplest anisotropic generalizations of the RW spacetime, viz., the Bianchi type I, V, and IX spacetimes. Then we constrain this model and its particular cases, viz., An-$Λ$CDM, $oΛ$CDM, and $Λ$CDM, by using the data sets from different probes, viz., Planck CMB(+Lens), BAO, SnIa Pantheon, and CC data, and discuss the results. Ultimately, we conclude that, within the setup under consideration, (i) the data confirm the spatial flatness and isotropic expansion, though a very small amount of present-day expansion anisotropy cannot be excluded, e.g., $Ω_{\sigma0}\lesssim10^{-18}$ (95\% C.L.) for An-$Λ$CDM from CMB+Lens, (ii) the introduction of spatial curvature or anisotropic expansion, or both, on top $Λ$CDM does not offer a possible relaxation to the $H_0$ tension, and (iii) the introduction of anisotropic expansion neither affects the closed space prediction from CMB(+Lens) nor does it improve the drastically reduced value of $H_0$ led by the closed space. We discuss why it is important and indispensable to maintain the geometric generalization work program, especially in models that offer solutions to cosmological tensions. [abridged]

astro-ph.CO

Report of the Topical Group on Cosmic Probes of Fundamental Physics for for Snowmass 2021

Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any other means, helping elucidate the underlying theory that completes the Standard Model. The last decade has witnessed a revolution of exciting discoveries such as the detection of high-energy neutrinos and gravitational waves. The scope for major developments in the next decades is dramatic, as we detail in this report.

hep-ph

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $σ_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,σ$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $Ω_m$, and the amplitude or rate of the growth of structure ($σ_8,fσ_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged]

astro-ph.CO

$Λ$CDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe

In this work, which follows a series of studies on the higher-dimensional steady state universe idea and prepared for Professor Tekin Dereli's Festschrift, we show the influence of the dynamical internal (unobservable) space on the evolution of the possible anisotropy of the external (observable) space. We obtain mathematically exactly the same Friedmann equation of the standard $Λ$CDM model for the external space, but with some remarkable physical differences. In particular, the higher-dimensional negative cosmological constant plays the role of the four-dimensional positive cosmological constant and the expansion anisotropy, viz., the shear scalar, of the external space mimics a negative cosmological constant; it would mimic a stiff fluid when allowed on top of the standard $Λ$CDM model. This latter feature gives us the opportunity to manipulate the CMB quadrupole temperature fluctuation, suggesting a possible answer to the fact that its observed value is lower than that predicted by the standard $Λ$CDM model.

gr-qc