arXiv subjects

Nobuyoshi Komatsu

Publications and source records attributed to Nobuyoshi Komatsu.

At least 19 recordsLinked to original sources

arXiv2026

Effective dissipative cosmology with $Λ$ from the first law of thermodynamics

We phenomenologically derive a cosmological model that includes both a cosmological constant term $Λ/3$ and a dissipative driving term $β(2 H^{2} + \dot{H})$ by applying both the first law of thermodynamics and an effective entropy (that is proportional to the Bekenstein--Hawking entropy) to matter creation cosmology. Here $H$, $\dot{H}$, and $β$ are the Hubble parameter, the time derivative of $H$, and a non-negative dimensionless coefficient used for the effective entropy, respectively. The dissipative term is proportional to the Ricci scalar curvature, suggesting that the dynamic creation pressure has the same dependence. We examine the model's background evolution in the late universe and its horizon thermodynamics. The present model supports a transition from a decelerating universe to an accelerating universe when $β<0.5$.The second law of thermodynamics is always satisfied on the horizon, and maximization of entropy is satisfied in the final stage. In addition, we study first-order density perturbations related to structure formation, by applying a neo-Newtonian approach to the present model. We then examine constraints on the present model using three types of observational data and the transitional and thermodynamic constraints and find that a weakly dissipative universe with $Λ$ is likely favored and consistent with our Universe. We also discuss irreversible entropy due to adiabatic particle creation, assuming a holographic-like matter creation cosmology.

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arXiv2025

Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model

The first and second laws of thermodynamics should lead to a consistent scenario for discussing the cosmological constant problem. In the present study, to establish such a thermodynamic scenario, cosmological equations in a flat Friedmann-Lemaître-Robertson-Walker universe were derived from the first law, using an arbitrary entropy $S_{H}$ on a cosmological horizon. Then, the cosmological equations were formulated based on a general formulation that includes two extra driving terms, $f_Λ(t)$ and $h_{\textrm{B}}(t)$, which are usually used for, e.g., time-varying $Λ(t)$ cosmology and bulk viscous cosmology, respectively. In addition, thermodynamic constraints on the two terms are examined using the second law of thermodynamics, extending a previous analysis [Phys. Rev. D 99, 043523 (2019) (arXiv:1810.11138)]. It is found that a deviation $S_Δ$ of $S_{H}$ from the Bekenstein-Hawking entropy plays important roles in the two terms. The second law should constrain the upper limits of $f_Λ(t)$ and $h_{\textrm{B}}(t)$ in our late Universe. The orders of the two terms are likely consistent with the order of the cosmological constant $Λ_{\textrm{obs}}$ measured by observations. In particular, when the deviation $S_Δ$ is close to zero, $h_{\textrm{B}}(t)$ and $f_Λ(t)$ should reduce to zero and a constant value (consistent with the order of $Λ_{\textrm{obs}}$), respectively, as if a consistent and viable scenario could be obtained from thermodynamics.

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arXiv2024

Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology

To clarify a holographic modified thermodynamic relation, the present study applies a general formulation for cosmological equations in a flat FLRW universe to the first law of thermodynamics, using the Bekenstein-Hawking entropy $S_{\rm{BH}}$ and a dynamical Kodama-Hayward temperature $T_{\rm{KH}}$. For the general formulation, both an effective pressure $p_{e}$ of cosmological fluids for dissipative universes (e.g., bulk viscous cosmology) and an extra driving term $f_Λ(t)$ for non-dissipative universes (e.g., time-varying $Λ(t)$ cosmology) are phenomenologically assumed. When $f_Λ(t)$ is constant, the modified thermodynamic relation is equivalent to the formulation of the first law in standard cosmology. One side of this modified relation describes thermodynamic quantities in the bulk and can be divided into two time-derivative terms, namely $\dotρ$ and $\dot{V}$ terms, where $ρ$ is the mass density of cosmological fluids and $V$ is the Hubble volume. Using the Gibbons-Hawking temperature $T_{\rm{GH}}$, the other side of this relation, $T_{\rm{KH}} \dot{S}_{\rm{BH}}$, can be formulated as the sum of $T_{\rm{GH}} \dot{S}_{\rm{BH}}$ and $[(T_{\rm{KH}}/T_{\rm{GH}}) -1] T_{\rm{GH}} \dot{S}_{\rm{BH}}$, which are equivalent to the $\dotρ$ and $\dot{V}$ terms, respectively, with the magnitude of the $\dot{V}$ term being proportional to the square of the $\dotρ$ term. In addition, the modified thermodynamic relation for constant $f_Λ(t)$ is examined by applying the equipartition law of energy on the horizon. This modified thermodynamic relation reduces to a kind of extended holographic-like connection when a constant $T_{\rm{KH}}$ universe is considered. The evolution of thermodynamic quantities is also discussed, using a constant $T_{\rm{KH}}$ model, extending a previous analysis [Phys. Rev. D 108, 083515 (2023) (arXiv:2306.11285)].

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arXiv2023

Cosmological model based on both holographic-like connection and Padmanabhan's holographic equipartition law

A cosmological model based on holographic scenarios is formulated in a flat Friedmann-Robertson-Walker universe. To formulate this model, the cosmological horizon is assumed to have a general entropy and a general temperature (including Bekenstein-Hawking entropy and Gibbons-Hawking temperature, respectively). In addition, a holographic-like connection [Eur. Phys. J. C 83, 690 (2023) (arXiv:2212.05822)] and Padmanabhan's holographic equipartition law are assumed for the entropy and temperature, and the Friedmann and acceleration equations are derived from these. The derived Friedmann and acceleration equations include both the entropy and the temperature and are slightly complicated, but can be combined into a single simple equation, corresponding to a similar equation that describes the background evolution of the universe in time-varying $Λ(t)$ cosmologies. The simple equation depends on the entropy but not on the temperature because the temperatures in the Friedmann and acceleration equations cancel each other. These results imply that the holographic-like connection should be consistent with Padmanabhan's holographic equipartition law through the present model and that the entropy plays a more important role. When the Gibbons-Hawking temperature is used as the temperature, the Friedmann and acceleration equations are found to be equivalent to those for a $Λ(t)$ model. A particular case of the present model is also examined, applying a power-law corrected entropy.

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arXiv2023

Evolution of thermodynamic quantities on cosmological horizon in $Λ(t)$ model

The horizon of a flat Friedmann--Robertson--Walker (FRW) universe is considered to be dynamic when the Hubble parameter $H$ and the Hubble radius $r_{H}$ vary with time, unlike for de Sitter universes. To clarify the thermodynamics on a dynamic horizon, the evolution of a dynamical Kodama--Hayward temperature and Bekenstein--Hawking entropy on the horizon of a flat FRW universe is examined in a $Λ(t)$ model similar to time-varying $Λ(t)$ cosmologies. The $Λ(t)$ model includes both a power-law term proportional to $H^α$ (where $α$ is a free variable) and the equation of state parameter $w$, extending a previous analysis [Phys. Rev. D 100, 123545 (2019) (arXiv:1911.08306)]. Using the present model, a matter-dominated universe ($w=0$) and a radiation-dominated universe ($w=1/3$) are examined, setting $α<2$. Both universes tend to approach de Sitter universes and satisfy the maximization of entropy in the last stage. The evolution of several parameters (such as the Bekenstein--Hawking entropy) is similar for both $w=0$ and $w=1/3$, though the dynamical temperature $T_{H}$ is different. In particular, $T_{H}$ is found to be constant when $w=1/3$ with $α=1$, although $H$ and $r_{H}$ vary with time. To discuss this case, the specific conditions required for constant $T_{H}$ are examined. Applying the specific condition to the present model gives a cosmological model that can describe a universe at constant $T_{H}$, as if the dynamic horizon is in contact with a heat bath. The relaxation processes for the universe are also discussed.

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arXiv2023

Horizon thermodynamics and cosmological equations: A holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk

Horizon thermodynamics is expected to be related to the effective energy based on the energy density calculated from the Friedmann equation for a Friedmann--Robertson--Walker (FRW) universe. In the present study, the effective energy and thermostatistical quantities on a cosmological horizon are examined to clarify the holographic-like connection between them, with a focus on a de Sitter universe. To this end, the Helmholtz free energy on the horizon is derived from horizon thermodynamics. The free energy is found to be equivalent to the effective energy calculated from the Friedmann equation. This consistency is interpreted as a kind of holographic-like connection. To examine this connection, Padmanabhan's holographic equipartition law, which is related to the origin of spacetime dynamics, is applied to a de Sitter universe. It is found that the law should lead to a holographic-like connection. The holographic-like connection is considered to be a bridge between thermostatistical quantities on the horizon and in the bulk. For example, cosmological equations for a flat FRW universe can be derived from horizon thermodynamics by accepting the connection as a viable scenario. In addition, a thermal entropy equivalent to the Bekenstein--Hawking entropy is obtained from the Friedmann equation using the concept of a canonical ensemble in statistical physics. The present study provides new insight into the discussion of horizon thermodynamics and cosmological equations.

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arXiv2022

Energy stored on a cosmological horizon and its thermodynamic fluctuations in holographic equipartition law

Our Universe is expected to finally approach a de Sitter universe whose horizon is considered to be in thermal equilibrium. In the present article, both the energy stored on the horizon and its thermodynamic fluctuations are examined through the holographic equipartition law. First, it is confirmed that a flat Friedmann--Robertson--Walker universe approaches a de Sitter universe, using a cosmological model close to lambda cold dark matter ($Λ$CDM) models. Then, based on the holographic equipartition law, the energy density of the Hubble volume is calculated from the energy on the Hubble horizon of a de Sitter universe. The energy density for a de Sitter universe is constant and the order of the energy density is consistent with the order of that for the observed cosmological constant. Second, thermodynamic fluctuations of energy on the horizon are examined, assuming stable fluctuations around thermal equilibrium states. A standard formulation of the fluctuations for a canonical ensemble is applied to the Hubble horizon of a de Sitter universe. The thermodynamic fluctuations of the energy are found to be a universal constant corresponding to the Planck energy, regardless of the Hubble parameter. In contrast, the relative fluctuations of the energy can be characterized by the ratio of the one-degree-of-freedom energy to the Planck energy. At the present time, the order of the relative fluctuations should be within the range of a discrepancy derived from a discussion of the cosmological constant problem, namely a range approximately from $10^{-60}$ to $10^{-123}$. The present results may imply that the energy stored on the Hubble horizon is related to a kind of effective dark energy, whereas the energy that can be `maximally' stored on the horizon may behave as if it were a kind of effective vacuum-like energy in an extended holographic equipartition law.

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arXiv2021

Evolution of dissipative and non-dissipative universes in holographic cosmological models with a power-law term

Density perturbations related to structure formations are expected to be different in dissipative and non-dissipative universes, even if the background evolution of the two universes is the same. To clarify the difference between the two universes, first-order density perturbations are studied, using two types of holographic cosmological models. The first type is a "$Λ(t)$ model" similar to a time-varying $Λ(t)$ cosmology for the non-dissipative universe. The second type is a "BV model" similar to a bulk viscous cosmology for the dissipative universe. To systematically examine the two different universes, a power-law term proportional to $H^α$ is applied to the $Λ(t)$ and BV (bulk-viscous-cosmology-like) models, assuming a flat Friedmann--Robertson--Walker model for the late universe. Here, $H$ is the Hubble parameter and $α$ is a free parameter whose value is a real number. The $Λ(t)$-$H^α$ and BV-$H^α$ models are used to examine first-order density perturbations for matter, in which the background evolution of the two models is equivalent. In addition, thermodynamic constraints on the two models are discussed, with a focus on the maximization of entropy on the horizon of the universe, extending previous analyses [Phys. Rev. D 100, 123545 (2019) (arXiv:1911.08306); 102, 063512 (2020) (arXiv:2006.09650)]. Consequently, the $Λ(t)$-$H^α$ model for small $|α|$ values is found to be consistent with observations and satisfies the thermodynamic constraints, compared with the BV-$H^α$ model. The results show that the non-dissipative universe described by the $Λ(t)$-$H^α$ model similar to lambda cold dark matter models is likely favored.

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arXiv2020

Entropy production due to adiabatic particle creation in a holographic dissipative cosmology

Cosmological adiabatic particle creation results in the generation of irreversible entropy. The evolution of this entropy is examined in a flat Friedmann--Robertson--Walker universe at late times, using a dissipative model with a power-law term (proportional to the power of the Hubble parameter $H$). In a dissipative universe, the irreversible entropy included in the Hubble volume is found to be proportional to $H^{-1}$, unlike for the case of the Bekenstein--Hawking entropy on the horizon of the universe. In addition, the evolution of the horizon entropy is examined, extending the previous analysis of a non-dissipative universe [Phys.\ Rev.\ D \textbf{100}, 123545 (2019) (arXiv:1911.08306)]. In the present model, the generalized second law of thermodynamics is always satisfied, whereas the maximization of entropy is satisfied under specific conditions. The dissipative universe should be constrained by the entropy maximization as if the universe behaves as an ordinary, isolated macroscopic system. The thermodynamic constraints are likely to be consistent with constraints on a transition from a decelerating universe to an accelerating universe.

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arXiv2019

Horizon thermodynamics in holographic cosmological models with a power-law term

Thermodynamics on the horizon of a flat universe at late times is studied in holographic cosmological models that assume an associated entropy on the horizon. In such models, a $Λ(t)$ model similar to a time-varying $Λ(t)$ cosmology is favored because of the consistency of energy flows across the horizon. Based on this consistency, a $Λ(t)$ model with a power-law term proportional to $H^α$ is formulated to systematically examine the evolution of the Bekenstein--Hawking entropy. Here, $H$ is the Hubble parameter and $α$ is a free parameter whose value is a real number. The present model always satisfies the second law of thermodynamics on the horizon. In particular, the universe for $α<2$ tends to approach thermodynamic equilibrium-like states. Consequently, when $α< 2$, the maximization of the entropy should be satisfied as well, at least in the last stage of the evolution of an expanding universe. A relaxation-like process before the last stage is also examined from a thermodynamics viewpoint.

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arXiv2019

Generalized thermodynamic constraints on holographic-principle-based cosmological scenarios

The holographic principle can lead to cosmological scenarios, i.e., holographic equipartition models. In this model, an extra driving term (corresponding to a time-varying cosmological term) in cosmological equations depends on an associated entropy on the horizon of the universe. The driving term is expected to be constrained by the second law of thermodynamics, as if the cosmological constant problem could be discussed from a thermodynamics viewpoint. In the present study, an arbitrary entropy on the horizon, $S_{H}$, is assumed, extending previous analysis based on particular entropies [Phys. Rev. D 96, 103507 (2017); (arXiv:1707.09101)]. The arbitrary entropy is applied to the holographic equipartition model, in order to universally examine thermodynamic constraints on the driving term in a flat Friedmann--Robertson--Walker universe at late times. The second law of thermodynamics for the holographic equipartition model is found to constrain the upper limit of the driving term, even if the arbitrary entropy is assumed. The upper limit implies that the order of the driving term is likely consistent with the order of the cosmological constant measured by observations. An approximately equivalent upper limit can be obtained from the positivity of $S_{H}$ in the holographic equipartition model.

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arXiv2017

Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy

A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the $α$-th power of the Hubble parameter, where $α$ is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constant-like when $α$ is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.

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arXiv2017

Cosmological model from the holographic equipartition law with a modified Rényi entropy

Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified Rényi entropy is applied to Padmanabhan's `holographic equipartition law', by regarding the Bekenstein--Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original Rényi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropic, and spatially flat universe. When a specific condition is mathematically satisfied, the extra driving term is found to be constant-like as if it is a cosmological constant. Interestingly, the order of the constant-like term is naturally consistent with the order of the cosmological constant measured by observations, because the specific condition constrains the value of the constant-like term.

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arXiv2016

General form of entropy on the horizon of the universe in entropic cosmology

Entropic cosmology assumes several forms of entropy on the horizon of the universe, where the entropy can be considered to behave as if it were related to the exchange (the transfer) of energy. To discuss this exchangeability, the consistency of the two continuity equations obtained from two different methods is examined, focusing on a homogeneous, isotropic, spatially flat, and matter-dominated universe. The first continuity equation is derived from the first law of thermodynamics, whereas the second equation is from the Friedmann and acceleration equations. To study the influence of forms of entropy on the consistency, a phenomenological entropic-force model is examined, using a general form of entropy proportional to the $n$-th power of the Hubble horizon. In this formulation, the Bekenstein entropy (an area entropy), the Tsallis--Cirto black-hole entropy (a volume entropy), and a quartic entropy are represented by $n=2$, $3$, and $4$, respectively. The two continuity equations for the present model are found to be consistent with each other, especially when $n=2$, i.e., the Bekenstein entropy. The exchange of energy between the bulk (the universe) and the boundary (the horizon of the universe) should be a viable scenario consistent with the holographic principle.

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arXiv2015

Cosmic microwave background radiation temperature in a dissipative universe

The relationship between the cosmic microwave background radiation temperature and the redshift, i.e., the $T$--$z$ relation, is examined in a phenomenological dissipative model. The model contains two constant terms, as if a nonzero cosmological constant $Λ$ and a dissipative process are operative in a homogeneous, isotropic, and spatially flat universe. The $T$--$z$ relation is derived from a general radiative temperature law, as appropriate for describing nonequilibrium states in a creation of cold dark matter (CCDM) model. Using this relation, the radiation temperature in the late universe is calculated as a function of a dissipation rate ranging from $\tildeμ =0$, corresponding to a nondissipative $Λ$CDM model, to $\tildeμ =1$, corresponding to a fully dissipative CCDM model. The $T$--$z$ relation for $\tildeμ =0$ is linear for standard cosmology and is consistent with observations. However, with increasing dissipation rate $\tildeμ$, the radiation temperature gradually deviates from a linear law because the effective equation-of-state parameter varies with time. When the background evolution of the universe agrees with a fine-tuned pure $Λ$CDM model, the $T$--$z$ relation for low $\tildeμ$ matches observations, whereas the $T$--$z$ relation for high $\tildeμ$ does not. Previous work also found that a weakly dissipative model accords with measurements of a growth rate for clustering related to structure formations. These results imply that low dissipation is likely for the universe. The weakly dissipative model should be further constrained by recent observations.

astro-ph.CO↗

arXiv2014

Entropic cosmology in a dissipative universe

The bulk viscosity of cosmological fluid and the creation of cold dark matter both result in the generation of irreversible entropy (related to dissipative processes) in a homogeneous and isotropic universe. To consider such effects, the general cosmological equations are reformulated, focusing on a spatially flat matter-dominated universe. A phenomenological entropic-force model is examined that includes constant terms as a function of the dissipation rate ranging from $\tildeμ =0$, corresponding to a nondissipative $Λ$CDM (lambda cold dark matter) model, to $\tildeμ =1$, corresponding to a fully-dissipative CCDM (creation of cold dark matter) model. A time evolution equation is derived for the matter density contrast, in order to characterize density perturbations in the present entropic-force model. It is found that the dissipation rate affects the density perturbations even if the background evolution of the late universe is equivalent to that of a fine-tuned pure $Λ$CDM model. With increasing dissipation rate $\tildeμ$, the calculated growth rate for the clustering gradually deviates from observations, especially at low redshifts. However, the growth rate for low $\tildeμ$ (less than 0.1) is found to agree well with measurements. A low-dissipation model predicts a smaller growth rate than does the pure $Λ$CDM model (for which $\tildeμ =0$). More detailed data are needed to distinguish the low-dissipation model from the pure $Λ$CDM one.

astro-ph.CO↗

arXiv2014

Evolution of the universe in entropic cosmologies via different formulations

We study two types of entropic-force models in a homogeneous, isotropic, spatially flat, matter-dominated universe. The first type is a `$Λ(t)$ type' similar to $Λ(t)$CDM (varying-lambda cold dark matter) models in which both the Friedmann equation and the acceleration equation include an extra driving term. The second type is a `BV type' similar to bulk viscous models in which the acceleration equation includes an extra driving term whereas the Friedmann equation does not. In order to examine the two types systematically, we consider an extended entropic-force model that includes a Hubble parameter ($H$) term and a constant term in entropic-force terms. The $H$ term is derived from a volume entropy whereas the constant term is derived from an entropy proportional to the square of an area entropy. Based on the extended entropic-force model, we examine four models obtained from combining the $H$ and constant terms with the $Λ(t)$ and BV types. The four models agree well with the observed supernova data and describe the background evolution of the late universe properly. However, the evolution of first-order density perturbations is different in each of the four models, especially for low redshift, assuming that an effective sound speed is negligible. The $Λ(t)$ type is found to be consistent with the observed growth rate of clustering, in contrast with the BV type examined in this study. A unified formulation is proposed as well, in order to examine density perturbations of the two types systematically.

astro-ph.CO↗

arXiv2013

Entropic cosmology for a generalized black-hole entropy

An entropic-force scenario, i.e., entropic cosmology, assumes that the horizon of the universe has an entropy and a temperature. In the present study, in order to examine entropic cosmology, we derive entropic-force terms not only from the Bekenstein entropy but also from a generalized black-hole entropy proposed by C. Tsallis and L.J.L. Cirto [Eur. Phys. J. C \textbf{73}, 2487 (2013)]. Unlike the Bekenstein entropy, which is proportional to area, the generalized entropy is proportional to volume because of appropriate nonadditive generalizations. The entropic-force term derived from the generalized entropy is found to behave as if it were an extra driving term for bulk viscous cosmology, in which a bulk viscosity of cosmological fluids is assumed. Using an effective description similar to bulk viscous cosmology, we formulate the modified Friedmann, acceleration, and continuity equations for entropic cosmology. Based on this formulation, we propose two entropic-force models derived from the Bekenstein and generalized entropies. In order to examine the properties of the two models, we consider a homogeneous, isotropic, and spatially flat universe, focusing on a single-fluid-dominated universe. The two entropic-force models agree well with the observed supernova data. Interestingly, the entropic-force model derived from the generalized entropy predicts a decelerating and accelerating universe, as for a fine-tuned standard $Λ$CDM (lambda cold dark matter) model, whereas the entropic-force model derived from the Bekenstein entropy predicts a uniformly accelerating universe.

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