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We study scalar field theories invariant under transverse diffeomorphisms incosmological contexts. We show that in the geometric optics approximation, thecorresponding particles move along geodesics and contribute with the sameactive mass (energy) to the gravitational field as in Diff invariant theories.However, for low-frequency modes, the contributions to the energy-momentumtensor differ from that of Diff invariant theories. This opens up a wide rangeof possibilities for cosmological model building. As an example, we show thatthe simplest TDiff invariant scalar field theory with only kinetic term coulddrive inflation and generate a red-tilted spectrum of density fluctuations. Wealso present a detailed analysis of cosmological perturbations and show thatthe breaking of full Diff invariance generically induces new non-adiabaticpressure perturbations. A simple scalar field dark matter model based on apurely kinetic term that exhibits the same clustering properties as standardcold dark matter is also presented.

TDiff invariant field theories for cosmology