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Andrewmiller5432

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- TL;DR Summary
- The authors were talking about path integral peaking around a single semiclassical history in specific bottom up cosmologies and then went on to say it doesn't work because path integral is appropriate for quantum cosmologies

Hi, I am new here so apologies if i am not using the right subforum. I don't have a physics background so i am not very technical but i do have a little bit of understanding. I was reading this paper by hawking/hertog and came across something that ended up confusing me.

Here is it:

"Pre-big bang cosmologies [10] are examples of models that are based on a bottomup approach. In these models one specifies an initial state on a surface in the infinite past and evolves this forward in time. A natural choice for the initial state would be flat space, but that would obviously remain flat space.

In particular, one finds that generic small perturbations at early times (or merely taking in account the remaining degrees of freedom) dramatically change the evolution nearthe transition. Rather than evolving towards an expanding semi-classical universe at late times, one generically produces a strong curvature singularity. Hence the evolution of pre-big bang cosmologies always includes a genuinely quantum gravitational phase, unless the initial state is extremely fine-tuned.

Now my questions is,

Isn't path integral always supposed to be about summing over all possibilities. What do they mean by "path integral peaking around a single semiclassical history" and describing cosmologies by a path integral in quantum cosmology rather than in terms of a single semi-classical trajectory. What is a path integral in terms of a single semi-classical trajectory?

Here is it:

"Pre-big bang cosmologies [10] are examples of models that are based on a bottomup approach. In these models one specifies an initial state on a surface in the infinite past and evolves this forward in time. A natural choice for the initial state would be flat space, but that would obviously remain flat space.

**Thus one instead starts withan unstable state in the infinite past, tuned carefully in order for the big crunch/bigbang transition to be smooth and the path integral to be peaked around a single semiclassical history**. Several explicit solutions of such bouncing cosmologies have beenfound in various minisuperspace approximations [14]. It has been shown, however, using several different techniques, that solutions of this kind are unstable [15, 16].In particular, one finds that generic small perturbations at early times (or merely taking in account the remaining degrees of freedom) dramatically change the evolution nearthe transition. Rather than evolving towards an expanding semi-classical universe at late times, one generically produces a strong curvature singularity. Hence the evolution of pre-big bang cosmologies always includes a genuinely quantum gravitational phase, unless the initial state is extremely fine-tuned.

**It is therefore more appropriate to describe these cosmologies by a path integral in quantum cosmology, and not in terms of a single semi-classical trajectory.**The universe won’t have a single history but every possible history, each with its own probability."Now my questions is,

Isn't path integral always supposed to be about summing over all possibilities. What do they mean by "path integral peaking around a single semiclassical history" and describing cosmologies by a path integral in quantum cosmology rather than in terms of a single semi-classical trajectory. What is a path integral in terms of a single semi-classical trajectory?