Motivated by quantum gravity we discuss a unified picture where both inflation and a present dynamical dark energy arise from the same scalar field. The history of the Universe describes a crossover from a „past fixed point“ where all particles are massless, to a „future fixed point“ where exact scale invariance is spontaneously broken, generating the particle masses. The cosmological solution can be extrapolated to the infinite past in physical time - the Universe has no beginning and no physical singularity. This is seen most easily in a frame where particle masses and the Planck mass are field-dependent and increase with time. In this „freeze frame“ the Universe shrinks and heats up during radiation and matter domination. In the equivalent, but singular Einstein frame cosmic history finds the familiar big bang description. A simple model is compatible with all present cosmological observations. It could be tested by the observation of huge lumps in the cosmic neutrino background , the detection of early dark energy , or rather large primordial graviton fluctuations generated during inflation.