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We present first-order post-Newtonian (1PN) approximations of a general imperfect fluid and of an axion as a coherently oscillating massive scalar field, both in the cosmological context. For the axion, using the Klein transformation and Madelung transformation we derive the Schr\"odinger and Madelung hydrodynamic formulations, respectively, in exact covariant way and to 1PN order. Complete sets of equations for the 1PN formulations are derived without fixing the temporal gauge condition. We study the linear instability in cosmology and a static limit for both fluid and axion; these are presented independently of the gauge condition to 1PN order, thus are naturally gauge-invariant., Comment: 18 pages, no figure

There currently exist limited and conflicting clinical data on the use of statins in coronavirus disease 2019 (COVID-19) patients. The aim of this paper was to compare hospitalized patients with COVID-19 who did and did not receive statins.We performed a population-based retrospective cohort study using South Korea's nationwide healthcare claim database. We identified consecutive patients hospitalized with COVID-19 and aged 40 years or older. Statin users were individuals with inpatient and outpatient prescription records of statins in the 240 days before cohort entry to capture patients who are chronic statin users and, therefore, receive statin prescriptions as infrequently as every 8 months. Our primary endpoint was a composite of all-cause death, intensive care unit (ICU) admission, mechanical ventilation use and cardiovascular outcomes [myocardial infarction (MI), transient cerebral ischemic attacks (TIA) or stroke]. We compared the risk of outcomes between statin users and non-users using logistic regression models after inverse probability of treatment weighting (IPTW) adjustment.Of 234,427 subjects in the database, 4,349 patients were hospitalized with COVID-19 and aged 40+ years. In total, 1,115 patients were statin users (mean age =65.9 years; 60% female), and 3,234 were non-users (mean age =58.3 years; 64% female). Pre-hospitalization statin use was not significantly associated with increased risk of the primary endpoint [IPTW odds ratio (OR) 0.82; 95% confidence interval (CI): 0.60-1.11]. Subgroup analysis showed a protective role of antecedent statin use for individuals with hypertension (IPTW OR 0.40; 95% CI: 0.23-0.69, P for interaction: 0.0087).Pre-hospitalization statin use is not detrimental and may be beneficial amongst hypertensive COVID-19 patients. Further investigation into statin is needed for more conclusive effects of statins for treatment of COVID-19.

Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In recent literature on using electromagnetic means to detect gravitational waves, an ad hoc definition based on regarding $F_{ab}$ with two covariant indices as the special relativistic one is popular. We show that by assigning physical fields to tensor components in that way, one cannot identify the frame four-vector allowing such a choice, thus failing to properly define the external charge and current densities in that frame. We propose the normal frame as the proper one. In this frame, the weak gravity corrections appear as the effective polarizations and magnetizations in both the homogeneous and inhomogeneous parts of Maxwell equations., 6 pages, no figure, published version in Annals of Physics

We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(\phi)$-coupling, and an axion as a massive scalar field with $\phi^2$-coupling, with the helical electromagnetic field. The $\alpha$-dynamo term appears naturally from the helical coupling in the MHD formulation. In the presence of the electromagnetic coupling, however, the Schr\"odinger and hydrodynamic formulations of the coherently oscillating axion are {\it not} available for the conventional $\phi$ coupling; instead, $\phi^2$ coupling allows successful formulations preserving the dark matter nature of the axion to nonlinear order. In the MHD formulation, direct couplings between the scalar and electromagnetic fields appear only for non-ideal MHD. We study gravitational and magnetic instabilities of the scalar field and axion MHDs., Comment: 7 pages, no figure

We present the general relativistic electrodynamics and magnetohydrodynamics with a helically coupled scalar field. We consider three component system with the fluid, scalar field and electromagnetic fields with the helical coupling. We derive three exact formulations: the covariant formulation, the ADM formulation, and the fully nonlinear and exact perturbation formulation. We also derive the weak-gravity limit with fully relativistic fluid and fields. The latter two formulations are presented in the cosmological context., Comment: 30 pages, no figure. Published in Physical Review D

There is uncertainty of the effect of immunosuppression, including corticosteroids, before COVID-19 infection on COVID-19 outcomes. The aim of this study was to investigate the relationship between prehospitalization immunosuppressants use (exposure) and COVID-19 patient outcomes.We conducted a population-based retrospective cohort study using a nationwide healthcare claims database of South Korea as of May 15, 2020. Confirmed COVID-19 infection in hospitalized individuals aged 40 years or older were included for analysis. We defined exposure variable by using inpatient and outpatient prescription records of immunosuppressants from the database. Our primary endpoint was a composite endpoint of all-cause death, intensive care unit (ICU) admission, and mechanical ventilation use. Inverse probability of treatment weighting (IPTW)-adjusted logistic regression analyses were used, to estimate odds ratio (OR) and 95% confidence intervals (CI), comparing immunosuppressants users and non-users.We identified 4,349 patients, for which 1,356 were immunosuppressants users and 2,993 were non-users. Patients who used immunosuppressants were at increased odds of the primary endpoint of all-cause death, ICU admission and mechanical ventilation use (IPTW OR =1.32; 95% CI: 1.06-1.63), driven by higher odds of all-cause mortality (IPTW OR =1.63; 95% CI: 1.21-2.26). Patients who used corticosteroids (n=1,340) were at increased odds of the primary endpoint (IPTW OR =1.33; 95% CI: 1.07-1.64).Immunosuppressant use was associated with worse outcomes among COVID-19 patients. These findings support the latest guidelines from the CDC that people on immunosuppressants are at high risk of severe COVID-19 and that immunocompromised people may benefit from booster COVID-19 vaccinations.

There currently exists a paucity of data on whether pre-admission anticoagulants use may have benefits among COVID-19 patients by preventing COVID-19 associated thromboembolism. The aim of this study was to assess the association between pre-admission anticoagulants use and COVID-19 adverse outcomes.We conducted a population-based cohort studying using the Health Insurance Review and Assessment Service (HIRA) claims data released by the South Korean government. Our study population consisted of South Koreans who were aged 40 years or older and hospitalized with COVID-19 between 1 January 2020 through 15 May 2020. We defined anticoagulants users as individuals with inpatient and outpatient prescription records in 120 days before cohort entry. Our primary endpoint was a composite of all-cause death, intensive care unit (ICU) admission, and mechanical ventilation use. Individual components of the primary endpoint were secondary endpoints. We compared the risk of endpoints between the anticoagulants users and non-users by logistic regression models, with the standardized mortality ratio weighting (SMRW) adjustment.In our cohort of 4,349 patients, for the primary endpoint of mortality, mechanical ventilation and ICU admission, no difference was noted between anticoagulants users and non-users (SMRW OR 1.11, 95% CI: 0.60-2.05). No differences were noted, among individual components. No effect modification was observed by age, sex, history of atrial fibrillation and thromboembolism, and history of cardiovascular disease. When applying the inverse probability of treatment weighting (IPTW) and SMRW with doubly robust methods in sensitivity analysis, anticoagulants use was associated with increased odds of the primary endpoint.Pre-admission anticoagulants were not determined to have a protective role against severe COVID-19 outcomes.

At second-order, scalar perturbations can source traceless and transverse perturbations to the metric, called induced gravitational waves (IGW). The apparent gauge-dependence of the IGW obscures the interpretation of the stochastic gravitational-wave signal. To elucidate the gauge dependence, we study the IGW from manifestly gauge-invariant scalar perturbations, namely, the relative velocity between the baryon and cold dark matter. From this relative velocity perturbation, we compute the dimensionless gravitational wave power spectrum and the corresponding expected angular power spectrum of the B-mode polarization of the cosmic microwave background. Although the effect turns out to be unobservably small, the calculation demonstrates both the importance of using observable quantities to remove the gauge ambiguity and the observable consequences of tensor perturbations which are not propagating gravitational waves., 12 pages, 3 figures; Published version: appendix expanded and typos corrected

SummaryPurposeThere is uncertainty of the effect of immunosuppression, including corticosteroids, before COVID-19 infection on COVID-19 outcomes. The aim of this study was to investigate the relationship between prehospitalization immunosuppressants use (exposure), and COVID-19 patient outcomes.MethodsWe conducted a population-based retrospective cohort study using a nationwide healthcare claims database of South Korea as of May 15, 2020. Confirmed COVID-19 infection in hospitalized individuals aged 40 years or older were included for analysis. We defined exposure variable by using inpatient and outpatient prescription records of immunosuppressants from the database. Our primary outcome was a composite endpoint of all-cause death, intensive care unit (ICU) admission, and mechanical ventilation use. Inverse probability of treatment weighting (IPTW)-adjusted logistic regression analyses were used, to estimate odds ratio (OR) and 95% confidence intervals, comparing immunosuppressants users and non-users.ResultsWe identified 4,349 patients, for which 1,356 were immunosuppressants users and 2,903 were non-users. Patients who used immunosuppressants were at increased odds of the primary outcome of all-cause death, ICU admission and mechanical ventilation use (IPTW OR 1.32; 95% CI: 1.06 – 1.63). Patients who used corticosteroids were at increased odds of the primary outcome (IPTW OR 1.33; 95% CI: 1.07 – 1.64).ConclusionWe support the latest guidelines from the CDC, that people on immunosuppressants are at high risk of severe COVID-19 and immunocompromised people may need booster COVID-19 vaccinations.FundingYGC’s work was partially supported by 2020R1G1A1A01006229 awarded by the National Research Foundation of Korea.

SummaryBackgroundThere currently exists limited and conflicting clinical data on the use of statins amongst COVID-19 patients. Given the both paucity and lack of consensus among data on statin’s efficacy and safety amongst COVID-19 patients, the current guideline is to continue statin in COVID-19 patients, who have previously been treated with statins. The aim of this paper was to compare hospitalized patients with COVID-19 who did and did not receive statins, in terms of COVID-19 outcomes.MethodsWe conducted population-based retrospective study using South Korea’s nationwide healthcare database as of May 15 2020. We identified 4,349 patients hospitalized with COVID-19 and aged 40 years or older. The cohort entry was defined as the date of hospitalization. Statin users were individuals with inpatient and outpatient prescription records of statins in the 240 days before cohort entry, and non-users were those without such records during this period. Our primary outcome was a composite endpoint of all-cause death, intensive care unit (ICU) admission, mechanical ventilation use and cardiovascular outcomes (myocardial infarction (MI), transient cerebral ischemic attacks (TIA) or stroke). We conducted inverse probability of treatment weighting (IPTW)-adjusted logistic regression analysis to estimate odds ratio (OR) and corresponding 95% confidence intervals (CI), to compare outcomes between statin users and non-users.Findings1,115 patients were statin users (mean age = 65.9 years; 60% female), and 3,234 were non-users (mean age = 58.3 years; 64% female). Statin use was not associated with increased risk of the primary outcome (IPTW OR 0.82; 95% CI: 0.60-1.11). Subgroup analysis showed a protective role of statins, for individuals with hypertension (IPTW OR 0.40; 95% CI: 0.23-0.69, p for interaction: 0.0087).InterpretationGiven that statins are not detrimental and that it may be beneficial amongst hypertensive patients and relatively cheap, we would encourage further investigation into statin for the prevention and treatment of COVID-19.FundingYGC’s work was partially supported by 2020R1G1A1A01006229 awarded by the National Research Foundation of Korea.Research in contextEvidence before this studyThere is limited and conflicting data reporting on statin use among COVID-19 patients, and its association with COVID-19 outcomesAdded value of this studyWe report no difference in COVID-19 outcomes between patients who used and did not use statins prior to COVID-19 diagnosis, except in hypertensive patients in which statins was shown to have a protective effect.Implications of all the available evidenceAs statins are not detrimental and relatively cheap, we encourage further investigation into statin for the prevention and treatment of COVID-19.

We derive oscillating gravitational potential caused by an ultralight axion as the cosmic dark matter, assuming the Compton wavelength smaller than the horizon scale. A new oscillatory term is found which dominates the previously known one on scales larger than the quantum Jeans-scale. In the context of linear perturbations in cosmology this new term might be more relevant in future observation. Both the quantum stress in density perturbation and the quantum oscillation of the gravitational potential are derived in the zero-shear gauge. We show that the axion fluid in relativistic analysis is quite different from the relativistic and Newtonian zero-pressure fluids, corresponding to Newtonian fluid only in the density perturbation. The consistency demands the relativistic analysis valid on scales larger than the Compton wavelength., Comment: 6 pages, no figure, substantial revisions made, including title

The cosmological principle (CP), assuming spatially homogeneous and isotropic background geometry in the cosmological scale, is a fundamental assumption in modern cosmology. Recent observations of the galaxy redshift survey provide relevant data to confront the principle with observation. We present a homogeneity test for the matter distribution using the BOSS DR12 CMASS galaxy sample and clarify the ontological status of the CP. As a homogeneity criterion, we compare the observed data with similarly constructed random distributions using the number count in the truncated cones method. Comparisons are also made with three theoretical results using the same method: (i) the dark matter halo mock catalogs from the N-body simulation, (ii) the log-normal distributions derived from the theoretical matter power spectrum, and (iii) direct estimation from the theoretical power spectrum. We show that the observed distribution is statistically impossible as a random distribution up to 300 Mpc/h in radius, which is around the largest statistically available scale. However, comparisons with the three theoretical results show that the observed distribution is consistent with these theoretically derived results based on the CP. We show that the observed galaxy distribution (light) and the simulated dark matter distribution (matter) are quite inhomogeneous even on a large scale. Here, we clarify that there is no inconsistency surrounding the ontological status of the CP in cosmology. In practice, the CP is applied to the metric and the metric fluctuation is extremely small in all cosmological scales. This allows the CP to be valid as the averaged background in metric. The matter fluctuation, however, is decoupled from the small nature of metric fluctuation in the subhorizon scale. What is directly related to the matter in Einstein's gravity is the curvature, a quadratic derivative of the metric., Comment: 12 pages, 13 figures, 1 table

We study gravito-magnetic instabilities of a static homogeneous medium with an aligned magnetic field in the two contexts of relativistic magnetohydrodynamics (MHD): first, MHD with post-Newtonian (PN) corrections, and second, special relativistic (SR) MHD with weak gravity. The analysis in the PN MHD is made without taking the temporal gauge condition, thus results are gauge-invariant. The PN corrections of the internal energy, pressure, sound velocity and the Alfv\'en velocity lower the critical (Jeans) wavelength. {All relativistic effects tend to destabilize the system.} Although the SR MHD with weak gravity is presented in the harmonic gauge, in the presence of gravity the stability analysis is strictly valid to Newtonian order. In the absence of gravity, the SR MHD is independent of the gauge condition. We present the plane wave velocities and the stability criteria in both cases., Comment: 10 pages, 4 figures

We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Proper solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the $L\geq 1$ modes should accompany the $L=0$ (homogeneous) mode for vanishing sound speed, $c_{s}$. For $c_{s}^{2}>1/5$ (a scalar field supported Einstein static model belongs to this case with $c_s^2 = 1$), the $L\geq 2$ modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable $L=0$ and $L=1$ modes., 19 pages, no figure, published in Phys. Rev. D

We present a fully nonlinear and exact perturbation formulation of Einstein's gravity with a general fluid and the ideal magnetohydrodynamics (MHD) without imposing the slicing (temporal gauge) condition. Using this formulation, we derive equations of special relativistic (SR) MHD in the presence of weak gravitation. The equations are consistently derived in the limit of weak gravity and action-at-a-distance in the maximal slicing. We show that in this approximation the relativistic nature of gravity does not affect the SR MHD dynamics, but SR effects manifest themselves in the metric, and thus gravitational lensing. Neglecting these SR effects may lead to an overestimation of lensing masses., Comment: 10 pages, no figure

We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear order. These additional contributions are comparable to the scalar-type purely relativistic perturbations, and thus negligible in the current paradigm of concordance cosmology: i.e., concerning density and velocity perturbations of the pressureless matter in perturbation regime well inside of matter-dominated epoch, we show that pure Einstein's gravity contributions appearing from the third order are entirely negligible (five orders of magnitude smaller than the Newtonian contributions) in all scales. We thus prove that Newtonian perturbation theory is quite reliable in calculating the amplitude of matter fluctuations even in the precision era of cosmology. Therefore, besides the ones imprinted as the initial condition generated in the earlier phase, the other relativistic effect relevant for interpreting observational data must be the projection effect that occurs when mapping galaxies on to the observed coordinate., Comment: 13 pages, 2 figures, the version accepted to be published in MNRAS

Newtonian cosmological perturbation equations valid to full nonlinear order are well known in the literature. Assuming the absence of the transverse-tracefree part of the metric, we present the general relativistic counterpart valid to full nonlinear order. The relativistic equations are presented without taking the slicing (temporal gauge) condition. The equations do have the proper Newtonian and first post-Newtonian limits. We also present the relativistic pressure correction terms in the Newtonian hydrodynamic equations., Comment: 7 pages, published in Nuclear Physics B (Proc. Suppl.)

We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations., Comment: 4 pages, no figure

The homogeneity of matter distribution at large scales, known as the cosmological principle, is a central assumption in the standard cosmological model. The case is testable though, thus no longer needs to be a principle. Here we perform a test for spatial homogeneity using the Sloan Digital Sky Survey Luminous Red Galaxies (LRG) sample by counting galaxies within a specified volume with the radius scale varying up to 300 Mpc/h. We directly confront the large-scale structure data with the definition of spatial homogeneity by comparing the averages and dispersions of galaxy number counts with allowed ranges of the random distribution with homogeneity. The LRG sample shows significantly larger dispersions of number counts than the random catalogues up to 300 Mpc/h scale, and even the average is located far outside the range allowed in the random distribution; the deviations are statistically impossible to be realized in the random distribution. This implies that the cosmological principle does not hold even at such large scales. The same analysis of mock galaxies derived from the N-body simulation, however, suggests that the LRG sample is consistent with the current paradigm of cosmology, thus the simulation is also not homogeneous in that scale. We conclude that the cosmological principle is not in the observed sky and nor is demanded to be there by the standard cosmological world model. This reveals the nature of the cosmological principle adopted in the modern cosmology paradigm, and opens new field of research in theoretical cosmology., Comment: 8 pages, 8 figures

The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\it general} hypersurface condition. Our formulation includes the anisotropic stress., Comment: 15 pages, no figure. Accepted in ApJ

We present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. Previously we consistently derived special relativistic hydrodynamic equations with weak gravity in Minkowski background. With the relativistic pressure and velocity one cannot derive the cosmological counterpart by a simple transformation from equations in the Minkowski background. Here we present a proper derivation. We point out the potential importance of relativistic pressure and velocity in gravitational lensing., Comment: 13 pages, no figure. Three new subsections (2.8-2.10) are added

The cosmic acceleration is one of the most significant cosmological discoveries over the last century. The two categories of explanation are exotic component (dark energy) and modified gravity. We constrain the two types of model by a joint analysis with perturbation growth and direct $H(z)$ data. Though the minimal $\chi^2$ of the $\Lambda$CDM is almost the same as that of DGP, in the sense of consistency we find that the dark energy ($\Lambda$CDM) model is more favored through a detailed comparison with the corresponding parameters fitted by expansion data., Comment: 10 pages, 6 figures, typo corrected

Recently we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. Here, we present results relaxing all the assumptions made in the previous works and present the general relativistic correction terms arising due to pressure, multi-component, background spatial curvature, and rotation. We show that even in the multi-component no general relativistic correction terms appear in the zero-pressure, irrotational fluids in a flat background. Thus, the relativistic/Newtonian correspondence of the density and velocity perturbations equations continues even in the multi-component situation. However, the pressure, background curvature, rotation lead to pure general relativistic correction terms to the second order. For the fluid including the pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the small-scale limit, to the second order, relativistic equations of density and velocity perturbations including the rotation coincide with the ones in Newton's gravity. We include the cosmological constant in the background world model which is consistent with the currently favored cosmology.

We investigate aspects of axion as a coherently oscillating massive classical scalar field by analyzing third order perturbations in Einstein's gravity in the axion-comoving gauge. The axion fluid has its characteristic pressure term leading to an axion Jeans scale which is cosmologically negligible for a canonical axion mass. Our classically derived axion pressure term in Einstein's gravity is identical to the one derived in the non-relativistic quantum mechanical context in the literature. We show that except for the axion pressure term, the axion fluid equations are exactly the same as the general relativistic continuity and Euler equations of a zero-pressure fluid up to third order perturbation. The general relativistic density and velocity perturbations of the CDM in the CDM-comoving gauge are exactly the same as the Newtonian perturbations to the second order (in all scales), and the pure general relativistic corrections appearing from the third order are numerically negligible (in all scales as well) in the current paradigm of concordance cosmology. Therefore, here we prove that, in the super-Jeans scale, the classical axion can be handled as the Newtonian CDM fluid up to third order perturbation. We also show that the axion fluid supports the vector-type (rotational) perturbation from the third order. Our analysis includes the cosmological constant., Comment: 16 pages, no figures

It is well known that couplings occur among the scalar-, vector-, and tensor-type perturbations of Friedmann world model in the second perturbational order. Here, we prove that, except for the gravitational wave contribution, the relativistic zero-pressure irrotational fluid perturbed to second order in a flat Friedmann background coincides exactly with the Newtonian result. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to the second order, our result has an important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches and even goes beyond the horizon. That is, our discovery shows that, in the zero-pressure case, except for the gravitational wave contribution, there are no relativistic correction terms even near and beyond the horizon to the second-order perturbation., Comment: 5 pages, no figure

We investigate the cosmological perturbations based on the f(R) gravity theory. Comparing the large angular scale CMBR observation we obtain several important constraints on the inflation model based on the f(R) gravity theory: the ordinary slow-roll assumption during the inflation with the Zel’dovich spectral conditions for the scalar and the tensor-type structures yields R2 gravity as the unique candidate. Also, the considered model predicts the nearly scale-invariant Zel’dovich spectra. We derive the strong constraints on the coupling constants of the R2 term and the energy scale during the inflation using the COBE-DMR observations. The result shows the gravitational wave contribution is very small. Therefore, future observations of the spectral indices and the gravitational wave contribution to CMBR temperature and polarization anisotropies will subject the current inflation models to a test.

We present a proof of the axion as a cold dark matter candidate to the fully nonlinear order perturbations based on Einstein's gravity. We consider the axion as a coherently oscillating massive classical scalar field without interaction. We present the fully nonlinear and exact, except for {\it ignoring} the transverse-tracefree tensor-type perturbation, hydrodynamic equations for an axion fluid in Einstein's gravity. We show that the axion has the characteristic pressure and anisotropic stress, the latter starts to appear from the second-order perturbation. But these terms do not directly affect the hydrodynamic equations in our axion treatment. Instead, what behaves as the effective pressure term in relativistic hydrodynamic equations is the perturbed lapse function and the relativistic result coincides exactly with the one known in the previous non-relativistic studies. The effective pressure term leads to a Jeans scale which is of the solar-system scale for conventional axion mass. As the fully nonlinear and relativistic hydrodynamic equations for an axion fluid coincide exactly with the ones of a zero-pressure fluid in the super-Jeans scale, we have proved the cold dark matter nature of such an axion in that scale., 6 pages, no figure

Einstein's gravity has the exact Newtonian limit as we take the infinite-speed-of-light limit in the zero-shear gauge and the uniform-expansion gauge. Although lacking proper Newtonian gravitational potential, here we show that Newtonian hydrodynamics for density and velocity is also recovered in the comoving gauge using the weak gravity and negligible pressure limits but without using the slow-motion and subhorizon conditions. This curious correspondence, however, is available only for the irrotational fluid.

We investigate observational consequences of the early episodically dominating dark energy on the evolution of cosmological structures. For this aim, we introduce the minimally coupled scalar field dark energy model with the Albrecht-Skordis potential which allows a sudden ephemeral domination of dark energy component during the radiation or early matter era. The conventional cosmological parameters in the presence of such an early dark energy are constrained with WMAP and Planck cosmic microwave background radiation data including other external data sets. It is shown that in the presence of such an early dark energy the estimated cosmological parameters can deviate substantially from the currently known $\Lambda\textrm{CDM}$-based parameters, with best-fit values differing by several percents for WMAP and by a percent level for Planck data. For the latter case, only a limited amount of dark energy with episodic nature is allowed since the Planck data strongly favors the $\Lambda\textrm{CDM}$ model. Compared with the conventional dark energy model, the early dark energy dominating near radiation-matter equality or at the early matter era results in the shorter cosmic age or the presence of tensor-type perturbation, respectively. Our analysis demonstrates that the alternative cosmological parameter estimation is allowed based on the same observations even in Einstein's gravity., Comment: 13 pages, 8 figures, 3 tables. Published in Phys. Rev. D

Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. Considering the general curvature ($K$) and the cosmological constant ($\Lambda$) in the background medium, the perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in general scales. In the first part, we elaborate these Newtonian correspondences. In the second part, using the identified gauge-invariant variables with correct Newtonian correspondences, we present the relativistic results with general pressures in the background and perturbation. We present the general super-sound-horizon scale solutions of the above mentioned variables valid for general $K$, $\Lambda$, and generally evolving equation of state. We show that, for vanishing $K$, the super-sound-horizon scale evolution is characterised by a conserved variable which is the perturbed three-space curvature in the comoving gauge. We also present equations for the multi-component hydrodynamic situation and for the rotation and gravitational wave., Comment: 16 pages, no figure, To appear in Gen. Rel. Grav

We present a general and unified formulation which can handle the classical evolution and quantum generation processes of cosmological scalar-type perturbations in a broad class of generalized gravity theories. Applications are made to the pole-like accelerated expansion stages purely driven by the coupling between the gravity and the dilaton field without referring to the potential term which are realized in a class of generalized gravity theories. We consider three such scenarios based on the scalar-tensor gravity, the induced gravity and the string theory. Vacuum fluctuations during the several expansion stages can be derived in exact analytic forms. Assuming that the pole-like acceleration stage provides a viable inflation scenario in the early universe, and assuming that the gravity theory transits to an Einstein one while the relevant scales remain in the superhorizon scale, we derive the generated classical density spectra. The generated classical density field shows a generic tilted spectrum with which differs from the observed spectrum supporting .

We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (\ref{mass-conservation-Mink})-(\ref{Poisson-eq-Mink}). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms {\it differ} from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation., JCAP in press, 11 pages

We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant., 16 pages, no figure

Versions of parameterized pseudo-Newtonian gravity theories specially designed for cosmology have been introduced in recent cosmology literature. The modifications often consider the zero-pressure fluid in the context of versions of modified Poisson-like equation with two different gravitational potentials or an effective gravitational constant. We consider such modifications available in the context of relativistic gravity theories where the action is a general algebraic function of the scalar curvature, the scalar field, and the kinetic term of the field. We show that in general it is not possible to isolate the fluid component even in Einstein's gravity. Only in the small-scale (far inside the horizon) limit, to the linear order, and assuming the quasistatic approximation, we can realize some special forms of the attempted modifications with limited validity. Theoretically motivated relativistic generalized gravity theories we are considering have much richer cosmological aspects than simply captured by some pseudo-Newtonian modifications. We show that even Einstein's gravity with a minimally coupled scalar field as a dynamical dark energy demands similar modification in Poisson's equation and the baryon density perturbation equation.

We prove that the axion as a coherently oscillating scalar field acts as a cold dark matter (CDM) to the second-order perturbations in all cosmological scales including the super-horizon scale. The proof is made in the axion-comoving gauge. For a canonical mass, the axion pressure term causes deviation from the CDM only on scales smaller than the Solar System size. Beyond such a small scale the equations of the axion fluid are the same as the ones of the CDM based on the CDM-comoving gauge which are exactly identical to the Newtonian equations to the second order. We also show that the axion fluid does not generate the rotational (vector-type) perturbation even to the second order. Thus, in the case of axion fluid, we have the relativistic/Newtonian correspondence to the second order, even considering the rotational perturbation. Our analysis is made in the presence of the cosmological constant, and can be easily extended to the realistic situation including other components of fluids and fields., Comment: Phys. Lett. B in press, 7 pages

We analyze the cosmological perturbations valid in a broad class of generalized gravity theories in a unified manner. A complete set of perturbation equations is derived in gauge-ready forms. We present general asymptotic solutions for several different choices of the gauge conditions in unified forms. As in the case of Einstein's gravity, the uniform-curvature gauge is particularly simple for treating the scalar-type perturbations in generalized gravity theories involving the scalar field and the scalar curvature. Remarkably, considering the growing mode in the uniform-curvature gauge, the same solutions derived in Einstein's gravity remain valid in a broad class of generalized gravity theories.

Axion as a coherently oscillating scalar field is known to behave as a cold dark matter in all cosmologically relevant scales. For conventional axion mass with 10^{-5} eV, the axion reveals a characteristic damping behavior in the evolution of density perturbations on scales smaller than the solar system size. The damping scale is inversely proportional to the square-root of the axion mass. We show that the axion mass smaller than 10^{-24} eV induces a significant damping in the baryonic density power spectrum in cosmologically relevant scales, thus deviating from the cold dark matter in the scale smaller than the axion Jeans scale. With such a small mass, however, our basic assumption about the coherently oscillating scalar field is broken in the early universe. This problem is shared by other dark matter models based on the Bose-Einstein condensate and the ultra-light scalar field. We introduce a simple model to avoid this problem by introducing evolving axion mass in the early universe, and present observational effects of present-day low-mass axion on the baryon density power spectrum, the cosmic microwave background radiation (CMB) temperature power spectrum, and the growth rate of baryon density perturbation. In our low-mass axion model we have a characteristic small-scale cutoff in the baryon density power spectrum below the axion Jeans scale. The small-scale deviations from the cold dark matter model in both matter and CMB power spectra clearly differ from the ones expected in the cold dark matter model mixed with the massive neutrinos as a hot dark matter component., 9 pages, 8 figures

In 1988 Bardeen has suggested a pragmatic formulation of cosmological perturbation theory which is powerful in practice to employ various fundamental gauge conditions easily depending on the character of the problem. The perturbation equations are presented without fixing the temporal gauge condition and are arranged so that one can easily impose fundamental gauge conditions by simply setting one of the perturbation variables in the equations equal to zero. In this way one can use the gauge degrees of freedom as an advantage in handling problems. Except for the synchronous gauge condition, all the other fundamental gauge conditions completely fix the gauge mode, and consequently, each variable in such a gauge has a unique gauge invariant counterpart, so that we can identify the variable as the gauge-invariant one. Here, we extend Bardeen's linear formulation to fully nonlinear order in perturbations, with the gauge advantage kept intact. Derived equations are exact, and from these we can easily expand to higher order perturbations in a gauge-ready form. We consider scalar- and vector-type perturbations of an ideal fluid in a flat background; we also present the multiple components of ideal fluid case. As applications we present fully nonlinear density and velocity perturbation equations in Einstein's gravity in the zero-pressure medium, vorticity generation from pure scalar-type perturbation, and fluid formulation of a minimally coupled scalar field, all in the comoving gauge. We also present the equation of gravitational waves generated from pure scalar- and vector-type perturbations., 23 pages, to appear in MNRAS

We compare the cosmological first-order post-Newtonian (1PN) approximation with the relativistic cosmological linear perturbation theory in a zero-pressure medium with the cosmological constant. We compare equations and solutions in several different gauge conditions available in both methods. In the PN method we have perturbation equations for density, velocity and gravitational potential independently of the gauge condition to 1PN order. However, correspondences with these 1PN equations are available only in certain gauge conditions in the perturbation theory. Equations of perturbed velocity and the perturbed gravitational potential in the zero-shear gauge exactly coincide with the Newtonian equations which remain valid even to 1PN order (the same is true for perturbed velocity in the comoving gauge), and equations of perturbed density in the zero-shear gauge and the uniform-expansion gauge coincide to 1PN order. We identify other correspondences available in different gauge conditions of the perturbation theory., 9 pages, submitted to ApJ

As is known above 90% of the energy content in Universe is made of unknown dark component. Usually this dark fluid is separated into two parts: dark matter and dark energy. However, it may be a mixture of these two energy components, or just one exotic unknown fluid. This property is dubbed as dark degeneracy. With this motivation, in this paper, a unified dark fluid having constant adiabatic sound speed $c_s^2=\alpha$, which is in the range $[0,1]$, is studied. At first, via the energy conservation equation, its energy density, $\rho_d/\rho_{d0}=(1-B_s)+B_s a^{-3(1+\alpha)}$ where $B_s$ is related to integration constant from energy conservation equation as another model parameter, is presented. Then by using Markov Chain Monte Carlo method with currently available cosmic observational data sets which include type Ia supernova Union 2, baryon acoustic oscillation and WMAP 7-year data of cosmic background radiation, we show that small values of $\alpha$ are favored in this unified dark fluid model. Furthermore, we show that smaller values of $\alpha, Comment: 9 pages, 5 figures

The decaying vacuum model (DV), treating dark energy as a varying vacuum, has been studied well recently. The vacuum energy decays linearly with the Hubble parameter in the late-times, $\rho_\Lambda(t) \propto H(t)$, and produces the additional matter component. We constrain the parameters of the DV model using the recent data-sets from supernovae, gamma-ray bursts, baryon acoustic oscillations, CMB, the Hubble rate and x-rays in galaxy clusters. It is found that the best fit of matter density contrast $\Omega_m$ in the DV model is much lager than that in $\Lambda$CDM model. We give the confidence contours in the $\Omega_m-h$ plane up to $3\sigma$ confidence level. Besides, the normalized likelihoods of $\Omega_m$ and $h$ are presented, respectively. %, Comment: 7 pages, 3 figures, accepted by European Physical Journal C

In this paper, a decay vacuum model ${\overline{\ensuremath{\rho}}}_{\ensuremath{\Lambda}}=3\ensuremath{\sigma}{M}_{p}^{2}{H}_{0}H$ is revisited by detailed analysis of background evolution and perturbation equations. We show the imprints on CMB temperature and matter power spectrum from the effective coupling terms between dark sectors by comparing to the standard cosmological constant model and observational data points (WMAP7 and SDSS DR7). We find that the decay vacuum model can describe the expansion rate at late times as well as the standard cosmological constant model but it fails to simultaneously reproduce the observed CMB and matter power spectrum. Its generalization ${\overline{\ensuremath{\rho}}}_{\ensuremath{\Lambda}}=3{M}_{p}^{2}({\ensuremath{\xi}}_{1}{H}_{0}H+{\ensuremath{\xi}}_{2}{H}^{2})$ is also discussed. Detailed analysis of the background evolution shows that the dimensionless parameter ${\ensuremath{\xi}}_{2}$ would be zero to avoid the unnatural ``fine-tuning'' and to keep the positivity of energy density of dark matter and dark energy in the early epoch.

The modified gravity with $f(R)=R^{1+\epsilon}$ ($\epsilon>0$) allows a scaling solution where the density of gravity sector follows the density of the dominant fluid. We present initial conditions of background and perturbation variables during the scaling evolution regime in the modified gravity. As a possible dark energy model we consider a gravity with a form $f(R)=R^{1+\epsilon}+qR^{-n}$ ($-1, Comment: 8 pages, 5 figures