Robertson Walker Cosmology Research Articles

Global dynamics of two models for Quintom Friedman–Lemaître–Robertson–Walker universes

We comprehensively analyse the dynamics for the gravitational field equations for the Chiral-Quintom theory in a Friedman–Lemaître–Robertson–Walker cosmology with an additional matter source. We consider a new set of dimensionless variables and write the field equations in the equivalent form of an algebraic-differential system. Specifically, we consider two families of quintom models where the two scalar fields interact in the kinetic sector. We mathematically focus on the dynamical effect of spatial curvature. Physically, we find two periods of inflation related to the Universe’s early and late-time acceleration phases.

Exiting Inflation with a Smooth Scale Factor

The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann–Robertson–Walker cosmology. We explore the consequences of imposing such a smoothness requirement, examining the forms of possible interpolating functions between the end of inflation and subsequent radiation- or matter-dominated eras, using a straightforward geometric model of the interpolating behavior. We quantify the magnitude of the cusp found in a direct transition from the end of slow-roll inflation to the subsequent era, analyze the validity of several smooth interpolator candidates, and investigate equation-of-state and thermodynamic constraints. We find an order-of-magnitude increase in the size of the universe at the end of the transition to a single-component radiation or matter era. We also evaluate the interpolating functions in terms of the standard theory of preheating and determine the effect on the number of bosons produced.

Nonzero spatial curvature in symmetric teleparallel cosmology

We consider the symmetric teleparallel fQ-gravity in Friedmann–Lemaître–Robertson–Walker cosmology with nonzero spatial curvature. For a nonlinear fQ model there exist always the limit of General Relativity with or without the cosmological constant term. The de Sitter solution is always provided by the theory and for the specific models fAQ≃Qαα−1,fBQ≃Q+f1Qαα−1 and fCQ≃Q+f1QlnQ it was found to be the unique attractor. Consequently small deviations from STGR can solve the flatness problem and lead to a de Sitter expansion without introduce a cosmological constant term. This result is different from that given by the power-law theories for the other two scalar of the trinity of General Relativity. What makes the nonlinear symmetric teleparallel theory to stand out are the new degree of freedom provided by the connection defined in the non-coincidence frame which describes the nonzero spatial curvature.

A resolution of the monopole problem in the Rh = ct Universe

Spontaneous symmetry breaking in grand unified theories is thought to have produced an exceedingly large number of magnetic monopoles in the early Universe. In the absence of suppression or annihilation, these very massive particles should be dominating the cosmic energy budget today, but none has ever been found. Inflation was invented in part to dilute their number, thereby rendering their density undetectable by current instruments. Should the inflationary paradigm not survive, however, the ensuing disagreement between theory and observation would constitute a cosmological ‘monopole problem’ and create further tension for any extension to the standard model of particle physics. But as is also true for all horizon problems, a monopole overabundance emerges only in cosmologies with an initial period of deceleration. We show that the alternative Friedmann–Lemaître–Robertson–Walker cosmology known as the Rh=ct universe completely eliminates all such anomalies rather trivially and naturally, without the need for an inflated expansion. We find that the monopole energy density today would be completely undetectable in Rh=ct. Evidence continues to grow that the zero active mass condition from general relativity ought to be an essential ingredient in ΛCDM.

Anisotropic solutions in symmetric teleparallel fleft( Qright) -theory: Kantowski–Sachs and Bianchi III LRS cosmologies

We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel fleft( Qright) -theory. For the background geometry we consider the Kantowski–Sachs and the Locally Rotationally Symmetric Bianchi type III geometries. These two anisotropic spacetimes are of special interest because in the limit of isotropy they are related to the closed and open Friedmann–Lemaître–Robertson–Walker cosmologies respectively. For each spacetime there exist two distinct families of flat, symmetric connections, which share the symmetries of the spacetime. We present the field equations, and from them, we determine the functional form of the fleft( Qright) Lagrangian which yields self-similar solutions. We initially consider the vacuum case and subsequently we introduce a matter source in terms of a perfect fluid. Last but not least, we report some self-similar solutions corresponding to static spherically symmetric spacetimes.

Unified dark energy from Chiral-Quintom model with a mixed potential in Friedmann–Lemaître–Robertson–Walker cosmology

For a spatially Friedmann–Lemaître–Robertson–Walker cosmology, we propose a multi-scalar field gravitational model. Specifically, we consider a two-scalar field cosmological model in which the kinetic components of the scalar fields establish a two-dimensional sphere of Lorentzian signature. For our Chiral-Quintom model we choose a mixed potential term Vleft( phi ,psi right) =V_{0}e^{lambda phi }+U_{0}e^{kappa phi }psi ^{frac{1}{sigma } } and we investigate the asymptotic limits of the cosmological parameters. This model for U_{0}=0, provides a generalization of the hyperbolic inflation where the equation of the state parameter can cross the phantom divide line. When U_{0}ne 0 we observe that this cosmological model exhibits asymptotic solutions that encompass accelerated universes, big rip singularities, and dust-like solutions. Hence, this multi-scalar field model it can be regarded as as a dark energy unify model which describes a variety of asymptotic cosmological scenarios.

The scale of homogeneity in the Rh = ct universe

ABSTRACT Studies of the Universe’s transition to smoothness in the context of Lambda cold dark matter (ΛCDM) have all pointed to a transition radius no larger than ∼300 Mpc. These are based on a broad array of tracers for the matter power spectrum, including galaxies, clusters, quasars, the Ly-α forest, and anisotropies in the cosmic microwave background. It is therefore surprising, if not anomalous, to find many structures extending out over scales as large as ∼2 Gpc, roughly an order of magnitude greater than expected. Such a disparity suggests that new physics may be contributing to the formation of large-scale structure, warranting a consideration of the alternative Friedmann–Lemaître–Robertson–Walker cosmology known as the Rh = ct universe. This model has successfully eliminated many other problems in ΛCDM. In this paper, we calculate the fractal (or Hausdorff) dimension in this cosmology as a function of distance, showing a transition to smoothness at ∼2.2 Gpc, fully accommodating all of the giant structures seen thus far. This outcome adds further observational support for Rh = ct over the standard model.

Inflation and Fractional Quantum Cosmology

The Wheeler–DeWitt equation for a flat and compact Friedmann–Lemaître–Robertson–Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the semiclassical regime and applying the Wentzel-Kramers-Brillouin (WKB) approximation, we show that some fascinating consequences are obtained for our simple fractional scenario that are completely different from their corresponding standard counterparts: (i) The conventional de Sitter behavior of the inflationary universe for constant potential is replaced by a power-law inflation. (ii) The non-locality of the Riesz’s fractional derivative produces a power-law inflation that depends on the fractal dimension of the compact spatial section of space-time, independent of the energy scale of the inflaton.

Constraining the Hubble constant and its lower limit from the proper motion of extragalactic radio jets

ABSTRACT The Hubble constant (H0) is a measurement to describe the expansion rate of the Universe in the current era. However, there is a 4.4σ discrepancy between the measurements from the early Universe and the late Universe. In this research, we propose a model-free and distance-free method to constrain H0. Combining Friedman–Lemaître–Robertson–Walker cosmology with geometrical relation of the proper motion of extragalactic jets, the lower limit (H0,min) of H0 can be determined using only three cosmology-free observables: the redshifts of the host galaxies, and the approaching and receding angular velocities of radio jets. Using these, we propose to use the Kolmogorov–Smirnov test (K–S test) between cumulative distribution functions of H0,min to differentiate cosmology. We simulate 100, 200, and 500 extragalactic jets with three levels of accuracy of the proper motion (μa and μr), at 10, 5, and 1 per cent, corresponding to the accuracies of the current and future radio interferometers. We perform K–S tests between the simulated samples as theoretical distributions with different H0 and power-law index of velocity distribution of jets and mock observational data. Our result suggests increasing sample sizes leads to tighter constraints on both power-law index and the Hubble constant at moderate accuracy (i.e. $10$ and $5{{\ \rm per\ cent}}$), while at $1{{\ \rm per\ cent}}$ accuracy, increasing sample sizes leads to tighter constraints on power-law index more. Improving accuracy results in better constraints in the Hubble constant compared with the power-law index in all cases, but it alleviates the degeneracy.

When can we compute analytically lookback time, age of the universe, and luminosity distance?

In Friedmann–Lemaître–Robertson–Walker cosmology, it is sometimes possible to compute analytically lookback time, age of the universe, and luminosity distance versus redshift, expressing them in terms of a finite number of elementary functions. We classify these situations using the Chebyshev theorem of integration and providing examples.

Well-defined equations of motion without constraining external sources

We present a new approach to constrained classical fields that enables the action formalism to dictate how external sources must enter the resulting equations of motion. If symmetries asserted upon the varied fields can be modeled as restrictions in Fourier space, we prove that these restrictions are automatically applied to external sources in an unambiguous way. In contrast, the typical procedure inserts symmetric ansatze into the Euler-Lagrange differential equations, even for external sources not being solved. This requires ad hoc constraint of external sources, which can introduce leading-order errors to model systems despite superficial consistency between model field and source terms. To demonstrate, we consider Robertson-Walker cosmologies within General Relativity and prove that the influence of point-like relativistic pressure sources on cosmological dynamics cannot be excluded by theoretical arguments.

Scale Symmetry and Friction

Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper, we will show through a series of examples how this symmetry extends to the space of couplings, as measured through observations of a system. This can be exploited to focus on observations that can be used to distinguish between different theories and identify those which give rise to identical physical evolutions. These can be reduced into a description that makes no reference to scale. The resultant systems can be derived from Herglotz’s principle and generally exhibit friction. Here, we will demonstrate this through three example systems: the Kepler problem, the N-body system and Friedmann–Lemaître–Robertson–Walker cosmology.

The anomalous 21-cm absorption at high redshifts

The EDGES collaboration has reported the detection of a global 21-cm signal with a plateau centered at 76 MHz (i.e., redshift 17.2), with an amplitude of 500^{+200}_{-500} mK. This anomalous measurement does not comport with standard cosmology, which can only accommodate an amplitude lesssim 230 mK. Nevertheless, the line profile’s redshift range (15lesssim zlesssim 20) suggests a possible link to Pop III star formation and an implied evolution out of the ‘dark ages.’ Given this tension with the standard model, we here examine whether the observed 21-cm signal is instead consistent with the results of recent modeling based on the alternative Friedmann–Lemaître–Robertson–Walker cosmology known as the R_{mathrm{h}}=ct universe, showing that – in this model – the CMB radiation might have been rethermalized by dust ejected into the IGM by the first-generation stars at redshift zsim 16. We find that the requirements for this process to have occurred would have self-consistently established an equilibrium spin temperature T_{mathrm{s}}approx 3.4 K in the neutral hydrogen, via the irradiation of the IGM by deep penetrating X-rays emitted at the termination shocks of Pop III supernova remnants. Such a dust scenario has been strongly ruled out for the standard model, so the spin temperature (sim 3.3 K) inferred from the 21-cm absorption feature appears to be much more consistent with the R_{mathrm{h}}=ct profile than that implied by Lambda CDM, for which adiabatic cooling would have established a spin temperature T_mathrm{s}(z=17.2)sim 6 K.

Observational constraints of bulk viscous Friedmann–Robertson–Walker cosmology with hybrid expansion law

In this work, we study bulk viscous Friedmann–Robertson–Walker cosmologies with hybrid expansion law. The bulk viscous theory of dissipative effects described by Eckart theory, truncated Israel–Stewart theory and full Israel–Stewart theory are implemented here. The hybrid expansion law model of scale factor is a general analytic type of evolution from which one can recover power-law and exponential expansion as a special cases. Hybrid expansion law model are applied to describe the present accelerating phase and early phases of evolution. We have determined the cosmological parameters such as Hubble parameter, deceleration parameter, jerk parameter, energy density, bulk viscous pressure and coefficient of bulk viscosity of the universe to construct physically acceptable cosmological model. We have considered both flat and closed space–time of Friedmann–Robertson–Walker cosmology to implement hybrid expansion law with dissipative effect. The variations of the coefficient of bulk viscosity with cosmic evolution are studied here in Eckart, truncated and full Israel–Stewart theory for flat and closed space–time to obtain physically acceptable hybrid expansion models driven by viscosity. We have also estimated observational constraints of the parameters of hybrid expansion law model by considering recent observational data set. We further reveal possible connections of our models with [Formula: see text] tension problem.

Global dynamics of Yang–Mills field and perfect-fluid Robertson–Walker cosmologies

We apply a new global dynamical system formulation to flat Robertson–Walker cosmologies with a massless and massive Yang–Mills field and a perfect-fluid with linear equation of state as the matter sources. This allows us to give proofs concerning the global dynamics of the models including asymptotic source-dominance toward the past and future time directions. For the pure massless Yang–Mills field, we also contextualize well-known explicit solutions in a global (compact) state space picture.

Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies

We obtain an explicit formula for the full expansion of the spectral action on Robertson–Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman–Kac formula. We then apply this result to the case of multifractal Packed Swiss Cheese Cosmology models obtained from an arrangement of Robertson–Walker spacetimes along an Apollonian sphere packing. Using Mellin transforms, we show that the asymptotic expansion of the spectral action contains the same terms as in the case of a single Robertson–Walker spacetime, but with zeta-regularized coefficients, given by values at integers of the zeta function of the fractal string of the radii of the sphere packing, as well as additional log-periodic correction terms arising from the poles (off the real line) of this zeta function.

Assessing cosmic acceleration with the Alcock–Paczyński effect in the SDSS-IV quasar catalogue

ABSTRACT The geometry of the Universe may be probed using the Alcock–Paczyński (AP) effect, in which the observed redshift size of a spherical distribution of sources relative to its angular size varies according to the assumed cosmological model. Past applications of this effect have been limited, however, by a paucity of suitable sources and mitigating astrophysical factors, such as internal redshift-space distortions and poorly known source evolution. In this Letter, we introduce a new test based on the AP effect that avoids the use of spatially bound systems, relying instead on sub-samples of quasars at redshifts z ≲ 1.5 in the Sloan Digital Sky Survey IV, with a possible extension to higher redshifts and improved precision when this catalogue is expanded by upcoming surveys. We here use this method to probe the redshift-dependent expansion rate in three pertinent Friedmann–Lemaître–Robertson–Walker cosmologies: Λ cold dark matter (ΛCDM), which predicts a transition from deceleration to acceleration at z ∼ 0.7; Einstein–de Sitter, in which the Universe is always decelerating; and the Rh = ct universe, which expands at a constant rate. ΛCDM is consistent with these data, but Rh = ct is favoured overall.

Equivalence principle on cosmological backgrounds in scalar–tensor theories

We study the extent up to which the equivalence principle is obeyed in models of modified gravity and dark energy involving a single scalar degree of freedom. We focus on the effective field theories of dark energy describing the late time acceleration in the presence of ordinary matter species. In their covariant form these coincide with the Horndeski theories on a cosmological background with a slowly varying Hubble rate and a time-dependent scalar field. We show that in the case of an exactly de Sitter universe both the weak and strong equivalence principles hold. This occurs due to the combination of the shift symmetry of the scalar and the time translational invariance of de Sitter space. When generalized to Friedmann–Robertson–Walker cosmologies (FRW) we show that the weak equivalence principle is obeyed for test particles and extended objects in the quasi-static subhorizon limit. We do this by studying the field created by an extended object moving in an FRW background as well as its equation of motion in an external gravitational field. We also estimate the corrections to the geodesic equation of the extended object due to the approximations made.

Modifying horizon thermodynamics by surface tensions

The modified first laws of thermodynamics at the black hole horizon and the cosmological horizon of the Schwarzschild de Sitter black hole and the apparent horizon of the Friedmann–Robertson–Walker cosmology are derived by the surface tensions, respectively. The corresponding Smarr relations are obeyed. For the black hole, the cosmological constant is first treated as a fixed constant, and then as a variable associated to the pressure. The law at the apparent horizon takes the same form as that at the cosmological horizon, but is different from that at the black hole horizon. The positive temperatures guarantee the appearance of the worked terms in the modified laws at the cosmological and apparent horizons. While they can disappear at the black hole horizon.

Cosmological perturbations in conformal gravity. II.

In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.