Can HAARP influence space, gravity and time as suggested by the article?
According to the paper cited, "High-power ELF radiation generated by modulated HF heating of the ionosphere can cause Earthquakes, Cyclones and localized heating", HAARP's power is 3.6 x 10^9 W
According to HAARP the actual power is 1000 times smaller than this - 3.6 x 10^6 W.
The Sun radiates 174 x 10^15 W onto the planet. Of this 35 x 10^15 W is absorbed by the atmosphere. Ref
So the Sun's radiation absorbed in the atmosphere is 10^9 times larger than HAARP, of course it is also over a much larger volume, so this needs to be taken into account ...
According to HAARP
The intensity of the HF signal in the ionosphere is less than 3 microwatts per cm2, tens of thousands of times less than the Sun's natural electromagnetic radiation reaching the earth and hundreds of times less than even the normal random variations in intensity of the Sun's natural ultraviolet (UV) energy which creates the ionosphere.
This is consistent with the known facts.
It therefore seems unlikely that HAARP has sufficient energy to cause significant earthquakes or cyclones. Nor to influence space, gravity or time in any novel or unusual ways.
Dr. Fran De Aquino's paper goes on to discuss his theory of gravitational shielding whereby a couple of people can render heavy rock monoliths weightless by draping them with a "gravitational shielding mantle" that multiplies the Sun's gravity. In my view, this confusion of topics rather undermines the credibility of the article.
Whatever harmful effects HAARP may be capable of, this paper does not seem a credible account of them.