Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring the expansion of the universe   We draw a figure from where it is possible to measure the number of e-folds
of expansion of the universe with a ruler. We find model independent bounds for
the number of e-folds during inflation, reheating and radiation. We also give a
lower bound to the size of the universe at the beginning of observable
inflation. Finally, we show that consistency with a relevant diagram requires
the existence of a new form of energy to drive the present expansion of the
universe.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat