Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNucleosynthesis in Power-Law Cosmologies
59
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We have recently considered cosmologies in which the Universal scale factor varies as a power of the age of the Universe and concluded that they cannot satisfy the observational constraints on the present age, the magnitude-redshift relation for SN Ia, and the primordial element (D, He3, He4, and Li7) abundances. This claim has been challenged in a proposal that suggested a high baryon density model (Omega_B*h*h = 0.3) with an expansion factor varing linearly with time could be consistent with the observed abundance of primoridal helium-4, while satisfying the age and magnitude-redshift constraints. In this paper we further explore primordial nucleosynthesis in generic power-law cosmologies, including the linear case, concluding that models selected to satisfy the other observational constraints are incapable of accounting for all the light element abundances.
rate research
Read More
In a class of models designed to solve the cosmological constant problem by coupling scalar or tensor classical fields to the space-time curvature, the universal scale factor grows as a power law in the age, $a propto t^alpha$, regardless of the matter content or cosmological epoch. We investigate constraints on such power-law cosmologies from the present age of the Universe, the magnitude-redshift relation, and from primordial nucleosynthesis. Constraints from the current age of the Universe and from the high-redshift supernovae data require large $alpha$ ($approx 1$), while consistency with the inferred primordial abundances of deuterium and helium-4 forces $alpha$ to lie in a very narrow range around a lower value ($approx 0.55$). Inconsistency between these independent cosmological constraints suggests that such power-law cosmologies are not viable.
Big bang nucleosynthesis (BBN) is affected by the energy density of a primordial magnetic field (PMF). For an easy derivation of constraints on models for PMF generations, we assume a PMF with a power law (PL) distribution in wave number defined with a field strength, a PL index, and maximum and minimum scales at a generation epoch. We then show a relation between PL-PMF parameters and the scale invariant (SI) strength of PMF for the first time. We perform a BBN calculation including PMF effects, and show abundances as a function of baryon to photon ratio $eta$. The SI strength of the PMF is constrained from observational constraints on abundances of $^4$He and D. The minimum abundance of $^7$Li/H as a function of $eta$ slightly moves to a higher $^7$Li/H value at a larger $eta$ value when a PMF exists during BBN. We then discuss degeneracies between the PL-PMF parameters in the PMF effect. In addition, we assume a general case in which both the existence and the dissipation of PMF are possible. It is then found that an upper limit on the SI strength of the PMF can be derived from a constraint on $^4$He abundance, and that a lower limit on the allowed $^7$Li abundance is significantly higher than those observed in metal-poor stars.
This paper studies seeded graph matching for power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of high-degree seeds in $1$-hop neighborhoods, we develop an efficient algorithm that exploits the low-degree seeds in suitably-defined $D$-hop neighborhoods. Specifically, we first match a set of vertex-pairs with appropriate degrees (which we refer to as the first slice) based on the number of low-degree seeds in their $D$-hop neighborhoods. This significantly reduces the number of initial seeds needed to trigger a cascading process to match the rest of the graphs. Under the Chung-Lu random graph model with $n$ vertices, max degree $Theta(sqrt{n})$, and the power-law exponent $2<beta<3$, we show that as soon as $D> frac{4-beta}{3-beta}$, by optimally choosing the first slice, with high probability our algorithm can correctly match a constant fraction of the true pairs without any error, provided with only $Omega((log n)^{4-beta})$ initial seeds. Our result achieves an exponential reduction in the seed size requirement, as the best previously known result requires $n^{1/2+epsilon}$ seeds (for any small constant $epsilon>0$). Performance evaluation with synthetic and real data further corroborates the improved performance of our algorithm.
A bootstrap percolation process on a graph $G$ is an infection process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours becomes infected and remains so forever. The parameter $rgeq 2$ is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse bootstrap percolation process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are $a(n)$ randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent $beta$, where $2 < beta < 3$, then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function $a_c(n)$ such that $a_c(n)=o(n)$ with the following property. Assuming that $n$ is the number of vertices of the underlying random graph, if $a(n) ll a_c(n)$, then the process does not evolve at all, with high probability as $n$ grows, whereas if $a(n)gg a_c(n)$, then there is a constant $eps>0$ such that, with high probability, the final set of infected vertices has size at least $eps n$. It turns out that when the maximum degree is $o(n^{1/(beta -1)})$, then $a_c(n)$ depends also on $r$. But when the maximum degree is $Theta (n^{1/(beta -1)})$, then $a_c (n)=n^{beta -2 over beta -1}$.
It is known that power-law k-inflation can be realized for the Lagrangian $P=Xg(Y)$, where $X=-(partial phi)^2/2$ is the kinetic energy of a scalar field $phi$ and $g$ is an arbitrary function in terms of $Y=Xe^{lambda phi/M_{pl}}$ ($lambda$ is a constant and $M_{pl}$ is the reduced Planck mass). In the presence of a vector field coupled to the inflaton with an exponential coupling $f(phi) propto e^{mu phi/M_{pl}}$, we show that the models with the Lagrangian $P=Xg(Y)$ generally give rise to anisotropic inflationary solutions with $Sigma/H=constant$, where $Sigma$ is an anisotropic shear and $H$ is an isotropic expansion rate. Provided these anisotropic solutions exist in the regime where the ratio $Sigma/H$ is much smaller than 1, they are stable attractors irrespective of the forms of $g(Y)$. We apply our results to concrete models of k-inflation such as the generalized dilatonic ghost condensate/the DBI model and we numerically show that the solutions with different initial conditions converge to the anisotropic power-law inflationary attractors. Even in the de Sitter limit ($lambda to 0$) such solutions can exist, but in this case the null energy condition is generally violated. The latter property is consistent with the Walds cosmic conjecture stating that the anisotropic hair does not survive on the de Sitter background in the presence of matter respecting the dominant/strong energy conditions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
