arXiv subjects

Tanmoy Paul

Publications and source records attributed to Tanmoy Paul.

At least 19 recordsLinked to original sources

arXiv2026

Fitting NANOGrav 15-year data and ACT data with modified inflation in entropic cosmology

Recent evidences of stochastic gravitational wave background (SGWB) through Pulsar Time Array (PTA) observations hint towards an alternative inflationary scenario, compared to the usual inflation, for describing the early stage of the universe in order to be compatible with the PTA data. Moreover, currently the Atacama Cosmology Telescope (combined with the Planck 2018 and BAO) refines the constraint on inflationary observables, compared to the only-Planck 2018 measurements. In the present work, we simultaneously address these two issues by incorporating certain modification during inflation over the usual inflationary scenario. Such modification amplifies the primordial tensor perturbation over the modes that are sensitive to the NANOGrav frequency region. For this purpose, we take the thermodynamic route of cosmology where the entropy of the apparent horizon is given by a generalized form of entropy that is able to generalize the other known form of horizon entropies for suitable representations. The constraints on the model parameters coming from the ACT data also fit the NANOGrav 15-year data (based on numerical analysis), which reveal the model's compatibility with both the ACT and the PTA data.

gr-qc↗

arXiv2026

Extension of $p$-compact operators in Banach spaces

We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these extension properties when the underlying spaces, either domain or codomain, are $P_λ$ spaces. We also answer if these extensions are almost norm-preserving in such circumstances where the extension $\widetilde{T}$ of a $T$ exists. It is observed that an operator can often be extended to a larger domain when the codomain is appropriately extended as well. Specific assumptions might enable us to obtain an extension of an operator that maintains the same range. Necessary and sufficient conditions are derived for a Banach space to be $L_1$-predual.

math.FA↗

arXiv2026

On Chebyshev centers in Banach spaces

In this note, we observe that $X\in (GC)$ if $X$ admits Chebyshev center for any finite set in it. This answers the problem raised by Veselý, addressed in [{\em Generalized centers of finite sets in Banach spaces}, Acta Math. Univ. Comenian. (N.S.) {\bf 66}(1) (1997), 83--115]. We extend our observation towards the fact that the property $(GC)$ is not a 3-space property.

math.FA↗

arXiv2025

Uniqueness of Hahn-Banach extensions in locally convex spaces

We intend to study the uniqueness of the Hahn-Banach extensions of linear functionals on a subspace in locally convex spaces. Various characterizations are derived when a subspace $Y$ has an analogous version of property-U (introduced by Phelps) in a locally convex space, referred to as the property-SNP. We characterize spaces where every subspace has this property. It is demonstrated that a subspace $M$ of a Banach space $E$ has property-U if and only if the subspace $M$ of the locally convex space $E$ endowed with the weak topology has the property-SNP, mentioned above. This investigation circles around exploring the potential connections between the family of seminorms and the unique extension of functionals previously mentioned. We extensively studied this property on the spaces of continuous functions on Tychonoff spaces endowed with the topology of pointwise convergence.

math.FA↗

arXiv2025

ACT inflation and its influence on reheating era in Einstein-Gauss-Bonnet gravity

We investigate the observational viability of non-minimally coupled scalar-Einstein-Gauss-Bonnet (GB) gravity, during inflation and post-inflationary reheating dynamics, from the perspective of the latest ACT-DR6 combined with the Planck 2018 and BAO data. It turns out that the ACT result considerably affects the inflationary e-fold number compared to the case where only Planck 2018 data is taken into account. The viable parameter spaces corresponding to the inflationary ACT-DR6+Planck18+BAO substantially influence the reheating phenomenology via the reheating equation of state ($w_\mathrm{eff}$) and the reheating temperature. In particular, the ACT-DR6+Planck18+BAO data seems to disfavor $w_\mathrm{eff} < 1/3$ during the reheating stage, which is unlike to that of only Planck 2018 case. These reveal how the ACT-DR6 data hits the early universe phenomenology from inflation to reheating in the context of higher curvature like scalar-Einstein-GB theory of gravity.

gr-qc↗

arXiv2025

Dark energy era with a resolution of Hubble tension in generalized entropic cosmology

We propose a new dark energy (DE) model from four parameter generalized entropy function of apparent horizon in a spatially flat universe. Such kind of generalized entropy is able to generalize all the known entropies proposed so far, for suitable representations of the entropic parameters. It turns out that the scenario can describe the correct thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing with the $Λ$CDM model, the proposed generalized entropic DE model provides a higher value of present Hubble parameter for certain range of entropic parameter(s) leading to a possible resolution of Hubble tension issue. We confront the scenario with CC, PantheonPlus+SH0ES, DESI DR1 and compressed Planck likelihood datasets, which clearly depicts the phenomenological viability of the present model for some best fitted values of entropic parameter(s) that are indeed consistent with the resolution of Hubble tension.

gr-qc↗

arXiv2025

Modified gravity as entropic cosmology

The present work reveals a direct correspondence between modified theories of gravity (cosmology) and entropic cosmology based on the thermodynamics of apparent horizon. It turns out that due to the total differentiable property of entropy, the usual thermodynamic law (used for Einstein gravity) needs to be generalized for modified gravity theories having more than one thermodynamic degrees of freedom (d.o.f.). For the modified theories having $n$ number of thermodynamic d.o.f., the corresponding horizon entropy is given by: $S_\mathrm{h} \sim S_\mathrm{BH} +$ terms containing the time derivatives of $S_\mathrm{BH}$ up to $(n-1)$-th order, and moreover, the coefficient(s) of the derivative term(s) are proportional to the modification parameter of the gravity theory (compared to the Einstein gravity; $S_\mathrm{BH}$ is the Bekenstein-Hawking entropy). By identifying the independent thermodynamic variables from the first law of thermodynamics, we show that the equivalent thermodynamic description of modified gravity naturally allows the time derivative of the Bekenstein-Hawking entropy in the horizon entropy.

gr-qc↗

arXiv2025

Order-preserving unique Hahn-Banach extensions

Let $X$ be a real Banach lattice with a unit, and let $Y \subseteq X$ be a closed subspace containing the unit. In this paper, we study the order-theoretic (also isometric) structure of $Y$ that it may inherit from $X$ under some additional conditions. Specifically, we consider the case where every continuous positive linear functional in the unit sphere of $Y^\ast$ admits a unique positive norm-preserving extension in $X^\ast$. Our results depend on the specific nature of the embedding of $Y$ in $X$. For a compact convex set $K$ with closed extreme boundary $\partial_e K$, for the restriction isometry of $A(K)$ (which is also order-preserving) into $C(\partial_e K)$, uniqueness of extensions of positive functionals leads to $K$ being a simplex and the restriction embedding being onto. In contrast, for a Choquet simplex $K$, we show that under the canonical embedding in the bidual $A(K)^{\ast\ast}$ (which is an abstract $M$-space), positive linear functionals having unique positive linear extensions imply that $K$ is a finite-dimensional simplex.

math.FA↗

arXiv2025

Generalized entropic dark energy with spatial curvature

In the realm of thermodynamics of apparent horizon, we construct a dark energy (DE) model from 4-parameter generalized entropy of apparent horizon in a spatially non-flat universe. In particular, considering a non-zero spatial curvature of the universe, we determine the dark energy fractional density and the dark energy equation of state (EoS) parameter (corresponding to the 4-parameter generalized entropy) in closed analytic forms. It turns out that the scenario can describe the correct thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing with the $Λ$CDM model, the proposed generalized entropic DE model provides a higher value of the present Hubble parameter for a certain range of entropic parameter(s) leading to a possible resolution of the Hubble tension issue. This in turn leads to a positive spatial curvature of the universe. We confront the scenario with CC \& BAO, Pantheon+ \& SH0ES and joint analysis of the CC \& BAO \& Pantheon+ \& SH0ES datasets, which clearly depicts the phenomenological viability of the present model for some best fitted values of entropic parameter(s) that are indeed consistent with the resolution of Hubble tension.

gr-qc↗

arXiv2025

Origin of bulk viscosity in cosmology and its thermodynamic implications

The purpose of the present work is two folded: (1) we propose a new mechanism for the origin of bulk viscosity in cosmological context, and then, (2) we address the thermodynamic implications of viscous cosmology based on the thermodynamics of apparent horizon. In particular, we show that the velocity gradient of the comoving expansion of the universe (along the distance measured from a comoving observer) in turn leads to a viscous like pressure of the fluid inside the apparent horizon. This points the importance of the bulk viscosity of fluid during the cosmological evolution of the universe, as the comoving expansion itself generates the viscosity. Therefore the thermodynamic interpretations of viscous cosmology becomes important from its own right. In this regard, it turns out that the cosmological evolution of the universe with a bulk viscosity $naturally$ satisfies the first and the second laws of thermodynamics of the apparent horizon, without imposing any exotic condition and for a general form of the coefficient of viscosity. This in turn affirms the thermodynamic correspondence of viscous cosmology.

gr-qc↗

arXiv2025

Natural validation of the second law of thermodynamics in cosmology

The present work shows that the second law of thermodynamics gets naturally satisfied during the entire cosmic evolution of the universe starting from inflation to the late dark energy era, without imposing any exotic condition. This makes the inter-connection between cosmology and thermodynamics more concrete. Consequently, it also depicts that why the matter fields are not in thermal equilibrium with the apparent horizon during most of the cosmic era of the universe, except for the fluids with $ω= -1/3$ leading to the transitions of the universe from an accelerating to a decelerating era and vice-versa.

gr-qc↗

arXiv2025

A study on $\mr{F}$-simultaneous approximative $τ$-compactness property in Banach spaces

Veselý (1997) studied Banach spaces that admit $f$-centers for finite subsets of the space. In this work, we introduce the concept of $\mr{F}$-simultaneous approximative $τ$-compactness property ($τ$-$\mr{F}$-SACP in short) for triplets $(X, V,\mf{F})$, where $X$ is a Banach space, $V$ is a $τ$-closed subset of $X$, $\mf{F}$ is a subfamily of closed and bounded subsets of $X$, $\mr{F}$ is a collection of functions, and $τ$ is the norm or weak topology on $X$. We characterize reflexive spaces with the Kadec-Klee property using triplets with $τ$-$\mr{F}$-SACP. We investigate the relationship between $τ$-$\mr{F}$-SACP and the continuity properties of the restricted $f$-center map. The study further examines $τ$-$\mr{F}$-SACP in the context of $CLUR$ spaces and explores various characterizations of $τ$-$\mr{F}$-SACP, including connections to reflexivity, Fréchet smoothness, and the Kadec-Klee property.

math.FA↗

arXiv2024

Different aspects of entropic cosmology

We give a short review of the recent developments of entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change of the entropy of the apparent horizon during the cosmic evolution of the universe, in particular, it is given by: $TdS = -d(ρV) + W dV$ (where $W$ is the work density and other quantities have their usual meaning). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question -- ``what will be the form of the horizon entropy corresponding to a general modified theory of gravity?'' The second law of horizon thermodynamics states that the change of total entropy (the sum of horizon entropy $+$ matter fields' entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of generalised entropy function.

gr-qc↗

arXiv2024

Primordial gravitational waves in horizon cosmology and constraints on entropic parameters

The hallmark of the 4-parameter generalized entropy is that it can represent various known entropies proposed so far for suitable limits of the parameters, and thus the 4-parameter generalized entropy can be applied on additive as well as on non-additive systems. Thereafter the proposal of the generalized entropy, it becomes important to constrain the corresponding parameters. In the present work, we intend to do this from the perspective of primordial gravitational waves (GWs) generated during inflation. In the background level, the generalized entropy successfully drives a viable and smooth evolution of the universe, particularly from inflation to reheating followed by a radiation era, for certain ranges of the entropic parameters. Consequently we investigate whether such viable ranges of the entropic parameters (coming from the background level) allow the primordial GWs spectrum to pass through the sensitivity curves of various GWs observatories. Therefore, if the future observatories can detect the signal of primordial GWs, then our theoretical expectation carried in the present work may provide a possible tool for the measurement of the generalized entropic parameters.

gr-qc↗

arXiv2024

f(R) gravity with spacetime torsion

The duality between a higher curvature $f(R)$ gravity model and a scalar-tensor theory helps to bring out the role of the additional degree of freedom originating from the higher derivative terms in the gravity action. Such a degree of freedom which appears as a scalar field has been shown to have multiple implications in Cosmological/Astrophysical scenario. The present work proposes a novel generalization to this correspondence between $f(R)$ gravity and a dual scalar-tensor theory when the affine connection is considered to have an antisymmetric part. It turns out that the $f(R)$ action in presence of spacetime torsion can be recast to a $non-minimally$ coupled scalar-tensor theory with a 2-rank massless antisymmetric tensor field in the Einstein frame, where the scalar field gets coupled with the antisymmetric field through derivative coupling(s).

gr-qc↗

arXiv2024

A study on various generalizations of Generalized centers $\bm{(GC)}$ in Banach spaces

In [{\em Generalized centers of finite sets in Banach spaces}, Acta Math. Univ. Comenian. (N.S.) {\bf 66}(1) (1997), 83--115], Veselý developed the idea of generalized centers for finite sets in Banach spaces. In this work, we explore the concept of {\it restricted $\mr{F}$-center property} for a triplet $(X,Y,\mc{F}(X))$, where $Y$ is a subspace of a Banach space $X$ and $\mc{F}(X)$ is the family of finite subsets of $X$. In addition, we generalize the analysis to include all closed, bounded subsets of $X$. Similar to how Lindenstrauss characterized $n.2.I.P.$, we characterize $n.X.I.P.$. So, it is possible to figure out that $Y$ has $n.X.I.P.$ in $X$ for all natural numbers $n$ if and only if $\tr{rad}_Y(F)=\tr{rad}_X(F)$ for all finite subsets $F$ of $Y$. It then turns out that, for all continuous, monotone functions $f$, the $f$-radii viz. $\tr{rad}_Y^f(F),\tr{rad}_X^f(F)$ are same whenever the generalized radii viz. $\tr{rad}_Y(F), \tr{rad}_X(F)$ are also same, for all finite subsets $F$ of $Y$. We establish a variety of characterizations of central subspaces of Banach spaces. With reference to an appropriate subfamily of closed and bounded subsets, it appears that a number of function spaces and subspaces exhibit the restricted weighted Chebyshev center property.

math.FA↗

arXiv2024

Second law of horizon thermodynamics during cosmic evolution

We examine the second law of thermodynamics in the context of horizon cosmology, in particular, whether the change of total entropy (i.e. the sum of the entropy for the apparent horizon and the entropy for the matter fields) proves to be positive with the cosmic expansion of the universe. The matter fields inside the horizon obey the thermodynamics of an open system as the matter fields has a flux through the apparent horizon, which is either outward or inward depending on the background cosmological dynamics. Regarding the entropy of the apparent horizon, we consider different forms of the horizon entropy like the Tsallis entropy, the Rényi entropy, the Kaniadakis entropy, or even the 4-parameter generalized entropy; and determine the appropriate conditions on the respective entropic parameters coming from the second law of horizon thermodynamics. The constraints on the entropic parameters are found in such a way that it validates the second law of thermodynamics during a wide range of cosmic era of the universe, particularly from inflation to radiation dominated epoch followed by a reheating stage. Importantly, the present work provides a model independent way to constrain the entropic parameters directly from the second law of thermodynamics for the apparent horizon.

gr-qc↗

arXiv2024

Tensor Perturbations from Bounce Inflation Scenario in f(Q) Gravity

In this paper, we construct a bounce inflation cosmological scenario in the framework of the modified symmetric teleparallel gravity, namely f(Q) theory, and investigate the tensor perturbations therein. As is well-known, the tensor perturbations generated in the very early Universe (inflation and pre-inflation regions) can account for the primordial gravitational waves (PGWs) that are to be detected by the next generation of GW experiments. We discuss the stability condition of the tensor perturbations in the bounce inflation process and investigate in detail the evolution of the perturbation variable. The general form of the tensor power spectrum is obtained both for large as well as small scale modes. As a result, we show for both kinds of modes (short or long wavelength modes), and the tensor spectrum may get a positive tilt in the parametric range where the tensor perturbation proves to be stable -- this interestingly hints an enhancement of gravitational waves' amplitude in the background of the f(Q) bounce-inflation scenario. Moreover, we study the LQC-like scenario as a specific case of our model, in which, the primordial tensor power spectrum turns out to be nearly scale-invariant on both small and large scales.

hep-th↗