2018年4月12日
Complete conformal classification of the Friedmann-Lemaitre-Robertson-Walker solutions with a linear equation of state
Classical and Quantum Gravity
- ,
- ,
- 巻
- 35
- 号
- 10
- 開始ページ
- 105011
- 終了ページ
- 105011
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1088/1361-6382/aab99f
- 出版者・発行元
- Institute of Physics Publishing
We completely classify Friedmann-Lemaĩtre-Robertson-Walker solutions with spatial curvature K = 0,±1 and equation of state p = wρ, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow φ <
0, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for w >
-1/3 and ρ >
0, while there is no bigbang singularity for w <
-1 and ρ >
0. For K = 0 or -1, -1 <
w <
-1/3 and ρ >
0, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for w <
-1 and ρ >
0, with null geodesics being future complete for -5/3 ≤ w <
-1 but incomplete for w <
-5/3. For w = -1/3, the expansion speed is constant. For -1 <
w <
-1/3 and K = 1, the universe contracts from infinity, then bounces and expands back to infinity. For K = 0, the past boundary consists of timelike infinity and a regular null hypersurface for -5/3 <
w <
-1, while it consists of past timelike and past null infinities for w ρ -5/3. For w <
-1 and K = 1, the spacetime contracts from an initial spacelike past bigrip singularity, then bounces and blows up at a final spacelike future big-rip singularity. For w <
-1 and K = -1, the past boundary consists of a regular null hypersurface. The trapping horizons are timelike, null and spacelike for w ϵ (-1, 1/3), w ϵ {1/3,-1} and w ϵ
(-∞,-1) ∪ (1/3,∞), respectively. A negative energy density (ρ <
0) is possible only for K = -1. In this case, for w >
-1/3, the universe contracts from infinity, then bounces and expands to infinity
for -1 <
w <
-1/3, it starts from a big-bang singularity and contracts to a big-crunch singularity
for w <
-1, it expands from a regular null hypersurface and contracts to another regular null hypersurface.
0, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for w >
-1/3 and ρ >
0, while there is no bigbang singularity for w <
-1 and ρ >
0. For K = 0 or -1, -1 <
w <
-1/3 and ρ >
0, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for w <
-1 and ρ >
0, with null geodesics being future complete for -5/3 ≤ w <
-1 but incomplete for w <
-5/3. For w = -1/3, the expansion speed is constant. For -1 <
w <
-1/3 and K = 1, the universe contracts from infinity, then bounces and expands back to infinity. For K = 0, the past boundary consists of timelike infinity and a regular null hypersurface for -5/3 <
w <
-1, while it consists of past timelike and past null infinities for w ρ -5/3. For w <
-1 and K = 1, the spacetime contracts from an initial spacelike past bigrip singularity, then bounces and blows up at a final spacelike future big-rip singularity. For w <
-1 and K = -1, the past boundary consists of a regular null hypersurface. The trapping horizons are timelike, null and spacelike for w ϵ (-1, 1/3), w ϵ {1/3,-1} and w ϵ
(-∞,-1) ∪ (1/3,∞), respectively. A negative energy density (ρ <
0) is possible only for K = -1. In this case, for w >
-1/3, the universe contracts from infinity, then bounces and expands to infinity
for -1 <
w <
-1/3, it starts from a big-bang singularity and contracts to a big-crunch singularity
for w <
-1, it expands from a regular null hypersurface and contracts to another regular null hypersurface.
- ID情報
-
- DOI : 10.1088/1361-6382/aab99f
- ISSN : 1361-6382
- ISSN : 0264-9381
- ORCIDのPut Code : 42991261
- SCOPUS ID : 85046631597