**1) The Cosmological Constant Problem
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**Scrutinizing the Cosmological Constant Problem and a possible resolution**

*abstract:*We suggest a new perspective on the Cosmological Constant Problem by scrutinizing its standard formulation. In classical and quantum mechanics without gravity, there is no definition of the zero point of energy. Furthermore, the Casimir effect only measures how the vacuum energy changes as one varies a geometric modulus. This leads us to propose that the physical vacuum energy in a Friedman-Lemaitre-Robertson-Walker expanding universe only depends on the time variation of the scale factor a(t). Equivalently, requiring that empty Minkowski space is stable is a principle that fixes the ambiguity in the zero point energy. We describe two different choices of vacuum, one of which is consistent with the current universe consisting only of matter and vacuum energy. The resulting vacuum energy density is proportional to (k_c H_0)^2, where k_c is a momentum cut-off and H_0 is the Hubble constant; for a cut-off close to the Planck scale, values of the vacuum energy density in agreement with astrophysical measurements are obtained. Another choice of vacuum is more relevant to the early universe consisting of only radiation and vacuum energy, and we suggest it as a possible model of inflation.

**2) Hidden-photon signal in the radio regime
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**Astrophysical searches for a hidden-photon signal in the radio regime**

*abstract:*Common extensions of the Standard Model of particle physics predict the existence of a “hidden” sector that comprises particles with a vanishing or very weak coupling to particles of the Standard Model (visible sector). For very light (m < 10^-14 eV) hidden U(1) gauge bosons (hidden photons), broad-band radio spectra of compact radio sources could be modified due to weak kinetic mixing with radio photons. Here, search methods are developed and their sensitivity discussed, with specific emphasis on the effect of the coherence length of the signal, instrumental bandwidth, and spectral resolution. We conclude that radio observations in the frequency range of 0.03–1400 GHz probe kinetic mixing of ~10^-3 of hidden photons with masses down to ~10^-17 eV. Prospects for improving the sensitivity with future radio astronomical facilities as well as by stacking data from multiple objects are discussed.