Probability for Primordial Black Holes in Higher Derivative Theories

Abstract

The probability for quantum creation of an inflationary universe with a pair of black holes in higher derivative theories has been studied. Considering a gravitational action which includes quadratic ($\alpha R^2$) and/or cubic term ($\beta R^3$) in scalar curvature in addition to a cosmological constant ($\Lambda$) in semiclassical approximation with Hartle-Hawking boundary condition, the probability has been evaluated. The action of the instanton responsible for creating such a universe, with spatial section with $S^{1}X{S}^2$ topology, is found to be less than that with a spatial $S^3$ topology, unless $\alpha <-\frac{1}{8\Lambda }$ in $R^2$-theory. In the $R^3$ theory, however, there exists a set of solutions without a cosmological constant when $\beta R^2=1$ and $\alpha =-3\sqrt{\beta }$ which admit primordial black holes (PBH) pair in an inflationary universe scenario. We note further that when $\beta R^2\ne 1$, one gets PBH pairs in the two cases : (i) with $\alpha$ and $\Lambda$ both positive and (ii) with $\Lambda$ positive and $\alpha$ negative satisfying a constraint $6|\alpha |\Lambda >1$. However, the relative probability for creation of an inflationary universe with a pair of black holes in the $R^3$-theory suppresses when $\alpha >-2\sqrt{\beta }$ or $|\alpha |<2\sqrt{\beta }$. However, if the above constraints are relaxed one derives interesting results leading to a universe with PBH in $R^3$-theory without cosmological constant. PACS No(s). : 04.20.Jb, 04.60.+n, 98.80.Hw

15 pages, No figures. accepted in Int. J. Mod. Phys. D (2001)

References in corpus (2)

• Open Inflation Without False Vacua
• Open Inflation, the Four Form and the Cosmological Constant

Cited by in corpus (5)

• Primordial Black Holes
• Fundamental Particle Structure in the Cosmological Dark Matter
• Primordial Black Hole Pair Creation Probability in Modified Gravitational Theory
• Probability for Primordial Black Holes Pair in 1/R Gravity
• Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms