MG14 - Talk detail

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We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single N th order Lovelock term in the action in d = 2N + 1, 2N + 2 dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. Pure Lovelock gravity also bears out the general feature that vacuum in odd dimensions d = 2N + 1 is kinematic; i.e. we may define an analogue Lovelock-Riemann tensor that vanishes in vacuum for d = 2N + 1, yet the Riemann curvature is non-zero. We analyze in detail the space of vacuum solutions for five and six dimensional pure Gauss-Bonnet theory. It possesses interesting and illuminating geometric structure and symmetries that carry over to the general case. We also comment on a closely related family of exponential solutions and on the possibility of solutions with complex Kasner exponents. The latter imply the existence of closed timelike curves in the geometry.

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The loop quantum dynamics of Kantowski-Sachs spacetime and the interior of higher genus black hole spacetimes with a cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmology. As in the other cases, though the quantum geometric effects resolve the physical singularity and result in a non-singular bounce, after the bounce a spacetime with small spacetime curvature does not emerge in either the subsequent backward or the forward evolution. Rather, in the asymptotic limit the spacetime manifold is a product of two constant curvature spaces. Interestingly, though the spacetime curvature of these asymptotic spacetimes is very high, their effective metric is a solution to the Einstein's field equations. Analysis of the components of the Ricci tensor shows that after the singularity resolution, the Kantowski-Sachs spacetime leads to an effective metric which can be interpreted as the `charged' Nariai, while the higher genus black hole interior can similarly be interpreted as anti Bertotti-Robinson spacetime with a cosmological constant. These spacetimes are `charged' in the sense that the energy momentum tensor that satisfies the Einstein's field equations is formally the same as the one for the uniform electromagnetic field, albeit it has a purely quantum geometric origin. The asymptotic spacetimes also have an emergent cosmological constant which is different in magnitude, and sometimes even its sign, from the cosmological constant in the Kantowski-Sachs and the interior of higher genus black hole metrics. With a fine tuning of the latter cosmological constant, we show that `uncharged' Nariai, and anti Bertotti-Robinson spacetimes with a vanishing emergent cosmological constant can also be obtained.

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It is well-known that Einstein gravity is kinematic (no non-trivial vacuum solution;i.e. Riemann vanishes whenever Ricci does so) in 3 dimension because Riemann is entirely given in terms of Ricci. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in action) gravity for which Nth order Lovelock Riemann tensor is indeed given in terms of corresponding Ricci for all odd d = 2N + 1 dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good discerning and guiding criterion for gravitational equation in higher dimensions.

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We argue that like velocity of light, Λ is a constant of spacetime, and these are the only two most fundamental constants of spacetime structure. Like gravitational field energy, vacuum en- ergy must gravitate but not through a stress tensor instead more subtly in line with the former by enlarging spacetime framework. Unfortunately this enlargement would not become visible until there comes about quantum theory of spacetime or gravity. One of possiblities could be that it gravitates through higher dimension. The important message that emrges is that Λ has therefore nothing to do with vacuum energy and hence is free to have any value as determeined by ac- celerating expansion of the Universe. The incorrigibly embarrassing number 10120 is therefore nothing but the statement that in units of the Planck area, the Universe measures as much!

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